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1.8 Lösning 5a - Versionshistorik
2026-07-15T07:23:01Z
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Taifun den 9 oktober 2015 kl. 10.34
2015-10-09T10:34:51Z
<p></p>
<table class='diff diff-contentalign-left'>
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<td colspan='2' style="background-color: white; color:black; text-align: center;">← Äldre version</td>
<td colspan='2' style="background-color: white; color:black; text-align: center;">Versionen från 9 oktober 2015 kl. 10.34</td>
</tr><tr><td colspan="2" class="diff-lineno">Rad 3:</td>
<td colspan="2" class="diff-lineno">Rad 3:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>                     \ln\,\left({x \over x-1}\right) & = 1                                        \; & &\;| \; e\,^{\cdot}              \\</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>                     \ln\,\left({x \over x-1}\right) & = 1                                        \; & &\;| \; e\,^{\cdot}              \\</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>                                       {x \over x-1} & = e                                        \; & &\;| \; \cdot (x-1)              \\</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>                                       {x \over x-1} & = e                                        \; & &\;| \; \cdot (x-1)              \\</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>                                     {\color{Red} x} & = e \cdot ({\color{Red} x} - 1)            \; & &\;: \;\text{OBS!} \; {\color{Red} x} \;\text{är obekanten medan}\;e\;\text{är en konstant. } \\</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>                                     {\color{Red} x} & = e \cdot ({\color{Red} x} - 1)            \; & &\;: \;\text{OBS!}\;{\color{Red} x} \;\text{är obekanten medan}\;e\;\text{är en konstant. } \\</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>                                     {\color{Red} x} & = e \cdot {\color{Red} x} - e              \; & &\;| \; + e                      \\</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>                                     {\color{Red} x} & = e \cdot {\color{Red} x} - e              \; & &\;| \; + e                      \\</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>                                 {\color{Red} x} + e & = e \cdot {\color{Red} x}                  \; & &\;| \; - {\color{Red} x}        \\</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>                                 {\color{Red} x} + e & = e \cdot {\color{Red} x}                  \; & &\;| \; - {\color{Red} x}        \\</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>                                                   e & = e \cdot {\color{Red} x} - {\color{Red} x} \; & &\;: \;\text{Bryt ut} \; {\color{Red} x} \;\text{i HL } \\</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>                                                   e & = e \cdot {\color{Red} x} - {\color{Red} x} \; & &\;: \;\text{Bryt ut}\;{\color{Red} x} \;\text{i HL } \\</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>                                                   e & = {\color{Red} x} \cdot (e - 1)            \; & &\;| \; / \; (e-1)                \\</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>                                                   e & = {\color{Red} x} \cdot (e - 1)            \; & &\;| \; / \; (e-1)                \\</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>                                       {e \over e-1} & = {\color{Red} x} \\</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>                                       {e \over e-1} & = {\color{Red} x} \\</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>                                     {\color{Red} x} & = {e \over e-1}  </div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>                                     {\color{Red} x} & = {e \over e-1}  </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>       \end{align}</math></div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>       \end{align}</math></div></td></tr>
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Taifun
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Taifun den 9 oktober 2015 kl. 10.31
2015-10-09T10:31:33Z
<p></p>
<table class='diff diff-contentalign-left'>
<col class='diff-marker' />
<col class='diff-content' />
<col class='diff-marker' />
<col class='diff-content' />
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<td colspan='2' style="background-color: white; color:black; text-align: center;">← Äldre version</td>
<td colspan='2' style="background-color: white; color:black; text-align: center;">Versionen från 9 oktober 2015 kl. 10.31</td>
</tr><tr><td colspan="2" class="diff-lineno">Rad 3:</td>
<td colspan="2" class="diff-lineno">Rad 3:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>                     \ln\,\left({x \over x-1}\right) & = 1                                        \; & &\;| \; e\,^{\cdot}              \\</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>                     \ln\,\left({x \over x-1}\right) & = 1                                        \; & &\;| \; e\,^{\cdot}              \\</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>                                       {x \over x-1} & = e                                        \; & &\;| \; \cdot (x-1)              \\</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>                                       {x \over x-1} & = e                                        \; & &\;| \; \cdot (x-1)              \\</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>                                     {\color{Red} x} & = e \cdot ({\color{Red} x} - 1)            \; & &\;: \;\text{OBS!} \; {\color{Red} x} \;\text{är obekanten medan e är en konstant. } \\</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>                                     {\color{Red} x} & = e \cdot ({\color{Red} x} - 1)            \; & &\;: \;\text{OBS!} \; {\color{Red} x} \;\text{är obekanten medan<ins class="diffchange diffchange-inline">}\;</ins>e<ins class="diffchange diffchange-inline">\;\text{</ins>är en konstant. } \\</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>                                     {\color{Red} x} & = e \cdot {\color{Red} x} - e              \; & &\;| \; + e                      \\</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>                                     {\color{Red} x} & = e \cdot {\color{Red} x} - e              \; & &\;| \; + e                      \\</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>                                 {\color{Red} x} + e & = e \cdot {\color{Red} x}                  \; & &\;| \; - {\color{Red} x}        \\</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>                                 {\color{Red} x} + e & = e \cdot {\color{Red} x}                  \; & &\;| \; - {\color{Red} x}        \\</div></td></tr>
</table>
Taifun
https://matte3c.mathonline.se/index.php?title=1.8_L%C3%B6sning_5a&diff=25116&oldid=prev
Taifun den 9 oktober 2015 kl. 10.29
2015-10-09T10:29:51Z
<p></p>
<table class='diff diff-contentalign-left'>
<col class='diff-marker' />
<col class='diff-content' />
<col class='diff-marker' />
<col class='diff-content' />
<tr style='vertical-align: top;'>
<td colspan='2' style="background-color: white; color:black; text-align: center;">← Äldre version</td>
<td colspan='2' style="background-color: white; color:black; text-align: center;">Versionen från 9 oktober 2015 kl. 10.29</td>
</tr><tr><td colspan="2" class="diff-lineno">Rad 3:</td>
<td colspan="2" class="diff-lineno">Rad 3:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>                     \ln\,\left({x \over x-1}\right) & = 1                                        \; & &\;| \; e\,^{\cdot}              \\</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>                     \ln\,\left({x \over x-1}\right) & = 1                                        \; & &\;| \; e\,^{\cdot}              \\</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>                                       {x \over x-1} & = e                                        \; & &\;| \; \cdot (x-1)              \\</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>                                       {x \over x-1} & = e                                        \; & &\;| \; \cdot (x-1)              \\</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>                                     {\color{Red} x} & = e \cdot ({\color{Red} x} - 1)            \; & &\;: \;\text{OBS!} \; {\color{Red} x} \;\text{är<del class="diffchange diffchange-inline">\;</del>obekanten<del class="diffchange diffchange-inline">\;</del>medan<del class="diffchange diffchange-inline">\;</del>e<del class="diffchange diffchange-inline">\;</del>är<del class="diffchange diffchange-inline">\;</del>en<del class="diffchange diffchange-inline">\;</del>konstant. } \\</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>                                     {\color{Red} x} & = e \cdot ({\color{Red} x} - 1)            \; & &\;: \;\text{OBS!} \; {\color{Red} x} \;\text{är obekanten medan e är en konstant. } \\</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>                                     {\color{Red} x} & = e \cdot {\color{Red} x} - e              \; & &\;| \; + e                      \\</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>                                     {\color{Red} x} & = e \cdot {\color{Red} x} - e              \; & &\;| \; + e                      \\</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>                                 {\color{Red} x} + e & = e \cdot {\color{Red} x}                  \; & &\;| \; - {\color{Red} x}        \\</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>                                 {\color{Red} x} + e & = e \cdot {\color{Red} x}                  \; & &\;| \; - {\color{Red} x}        \\</div></td></tr>
</table>
Taifun
https://matte3c.mathonline.se/index.php?title=1.8_L%C3%B6sning_5a&diff=25115&oldid=prev
Taifun den 9 oktober 2015 kl. 10.29
2015-10-09T10:29:09Z
<p></p>
<table class='diff diff-contentalign-left'>
<col class='diff-marker' />
<col class='diff-content' />
<col class='diff-marker' />
<col class='diff-content' />
<tr style='vertical-align: top;'>
<td colspan='2' style="background-color: white; color:black; text-align: center;">← Äldre version</td>
<td colspan='2' style="background-color: white; color:black; text-align: center;">Versionen från 9 oktober 2015 kl. 10.29</td>
</tr><tr><td colspan="2" class="diff-lineno">Rad 3:</td>
<td colspan="2" class="diff-lineno">Rad 3:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>                     \ln\,\left({x \over x-1}\right) & = 1                                        \; & &\;| \; e\,^{\cdot}              \\</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>                     \ln\,\left({x \over x-1}\right) & = 1                                        \; & &\;| \; e\,^{\cdot}              \\</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>                                       {x \over x-1} & = e                                        \; & &\;| \; \cdot (x-1)              \\</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>                                       {x \over x-1} & = e                                        \; & &\;| \; \cdot (x-1)              \\</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>                                     {\color{Red} x} & = e \cdot ({\color{Red} x} - 1)            \; & &\;: \;\text{<del class="diffchange diffchange-inline">Bryt ut</del>} \; {\color{Red} x} \;\text{<del class="diffchange diffchange-inline">i HL </del>} \\</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>                                     {\color{Red} x} & = e \cdot ({\color{Red} x} - 1)            \; & &\;: \;\text{<ins class="diffchange diffchange-inline">OBS!</ins>} \; {\color{Red} x} \;\text{<ins class="diffchange diffchange-inline">är\;obekanten\;medan\;e\;är\;en\;konstant. </ins>} \\</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>                                     {\color{Red} x} & = e \cdot {\color{Red} x} - e              \; & &\;| \; + e                      \\</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>                                     {\color{Red} x} & = e \cdot {\color{Red} x} - e              \; & &\;| \; + e                      \\</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>                                 {\color{Red} x} + e & = e \cdot {\color{Red} x}                  \; & &\;| \; - {\color{Red} x}        \\</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>                                 {\color{Red} x} + e & = e \cdot {\color{Red} x}                  \; & &\;| \; - {\color{Red} x}        \\</div></td></tr>
</table>
Taifun
https://matte3c.mathonline.se/index.php?title=1.8_L%C3%B6sning_5a&diff=25114&oldid=prev
Taifun den 9 oktober 2015 kl. 10.27
2015-10-09T10:27:20Z
<p></p>
<table class='diff diff-contentalign-left'>
<col class='diff-marker' />
<col class='diff-content' />
<col class='diff-marker' />
<col class='diff-content' />
<tr style='vertical-align: top;'>
<td colspan='2' style="background-color: white; color:black; text-align: center;">← Äldre version</td>
<td colspan='2' style="background-color: white; color:black; text-align: center;">Versionen från 9 oktober 2015 kl. 10.27</td>
</tr><tr><td colspan="2" class="diff-lineno">Rad 3:</td>
<td colspan="2" class="diff-lineno">Rad 3:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>                     \ln\,\left({x \over x-1}\right) & = 1                                        \; & &\;| \; e\,^{\cdot}              \\</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>                     \ln\,\left({x \over x-1}\right) & = 1                                        \; & &\;| \; e\,^{\cdot}              \\</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>                                       {x \over x-1} & = e                                        \; & &\;| \; \cdot (x-1)              \\</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>                                       {x \over x-1} & = e                                        \; & &\;| \; \cdot (x-1)              \\</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>                                     {\color{Red} x} & = e \cdot ({\color{Red} x} - 1) <del class="diffchange diffchange-inline">                                                  </del>\\</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>                                     {\color{Red} x} & = e \cdot ({\color{Red} x} - 1) <ins class="diffchange diffchange-inline">            \; & &\;: \;\text{Bryt ut} \; {\color{Red} x} \;\text{i HL } </ins>\\</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>                                     {\color{Red} x} & = e \cdot {\color{Red} x} - e              \; & &\;| \; + e                      \\</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>                                     {\color{Red} x} & = e \cdot {\color{Red} x} - e              \; & &\;| \; + e                      \\</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>                                 {\color{Red} x} + e & = e \cdot {\color{Red} x}                  \; & &\;| \; - {\color{Red} x}        \\</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>                                 {\color{Red} x} + e & = e \cdot {\color{Red} x}                  \; & &\;| \; - {\color{Red} x}        \\</div></td></tr>
</table>
Taifun
https://matte3c.mathonline.se/index.php?title=1.8_L%C3%B6sning_5a&diff=25113&oldid=prev
Taifun den 9 oktober 2015 kl. 10.17
2015-10-09T10:17:21Z
<p></p>
<table class='diff diff-contentalign-left'>
<col class='diff-marker' />
<col class='diff-content' />
<col class='diff-marker' />
<col class='diff-content' />
<tr style='vertical-align: top;'>
<td colspan='2' style="background-color: white; color:black; text-align: center;">← Äldre version</td>
<td colspan='2' style="background-color: white; color:black; text-align: center;">Versionen från 9 oktober 2015 kl. 10.17</td>
</tr><tr><td colspan="2" class="diff-lineno">Rad 1:</td>
<td colspan="2" class="diff-lineno">Rad 1:</td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>::<math>\begin{align} \ln\,x                        & = 1 + \ln\,(x-1) \; & &\;| \; - \ln\,(x-1) \\</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>::<math>\begin{align} \ln\,x                        & = 1 + \ln\,(x-1) <ins class="diffchange diffchange-inline">                          </ins>\; & &\;| \; - \ln\,(x-1) <ins class="diffchange diffchange-inline">            </ins>\\</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>                     \ln\,x - \ln\,(x-1)            & = 1 <del class="diffchange diffchange-inline">            </del>\; & &\;: \;\text{Logaritmlag 2 i VL}  \\</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>                     \ln\,x - \ln\,(x-1)            & = 1 <ins class="diffchange diffchange-inline">                                        </ins>\; & &\;: \;\text{Logaritmlag 2 i VL}  \\</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>                     \ln\,\left({x \over x-1}\right) & = 1 \; & &\;| \; e\,^{\cdot} <del class="diffchange diffchange-inline">              </del>\\</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>                     \ln\,\left({x \over x-1}\right) & = 1 <ins class="diffchange diffchange-inline">                                        </ins>\; & &\;| \; e\,^{\cdot} <ins class="diffchange diffchange-inline">              </ins>\\</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>                                       {x \over x-1} & = e \; & &\;| \; \cdot (x-1) <del class="diffchange diffchange-inline">              </del>\\</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>                                       {x \over x-1} & = e <ins class="diffchange diffchange-inline">                                        </ins>\; & &\;| \; \cdot (x-1) <ins class="diffchange diffchange-inline">              </ins>\\</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>                                     {\color{Red} x} & = e \cdot ({\color{Red} x} - 1) <del class="diffchange diffchange-inline">            </del>\\</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>                                     {\color{Red} x} & = e \cdot ({\color{Red} x} - 1) <ins class="diffchange diffchange-inline">                                                  </ins>\\</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>                                     {\color{Red} x} & = e \cdot {\color{Red} x} - e \; <del class="diffchange diffchange-inline">  </del>& &\;| \; + e <del class="diffchange diffchange-inline"> </del>\\</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>                                     {\color{Red} x} & = e \cdot {\color{Red} x} - e <ins class="diffchange diffchange-inline">              </ins>\; & &\;| \; + e <ins class="diffchange diffchange-inline">                      </ins>\\</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>                                 {\color{Red} x} + e & = e \cdot {\color{Red} x} <del class="diffchange diffchange-inline">    </del>\; <del class="diffchange diffchange-inline">  </del>& &\;| \; - {\color{Red} x} \\</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>                                 {\color{Red} x} + e & = e \cdot {\color{Red} x} <ins class="diffchange diffchange-inline">                  </ins>\; & &\;| \; - {\color{Red} x} <ins class="diffchange diffchange-inline">        </ins>\\</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>                                                   e & = e \cdot {\color{Red} x} - {\color{Red} x} \; & &\;: \;\text{Bryt ut} \; {\color{Red} x} \;\text{i HL } \\</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>                                                   e & = e \cdot {\color{Red} x} - {\color{Red} x} \; & &\;: \;\text{Bryt ut} \; {\color{Red} x} \;\text{i HL } \\</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>                                                   e & = {\color{Red} x} \cdot (e - 1) \; & &\;| \; / \; (e-1) \\</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>                                                   e & = {\color{Red} x} \cdot (e - 1) <ins class="diffchange diffchange-inline">            </ins>\; & &\;| \; / \; (e-1) <ins class="diffchange diffchange-inline">              </ins>\\</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>                                       {e \over e-1} & = {\color{Red} x} \\</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>                                       {e \over e-1} & = {\color{Red} x} \\</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>                                     {\color{Red} x} & = {e \over e-1}  </div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>                                     {\color{Red} x} & = {e \over e-1}  </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>       \end{align}</math></div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>       \end{align}</math></div></td></tr>
</table>
Taifun
https://matte3c.mathonline.se/index.php?title=1.8_L%C3%B6sning_5a&diff=25112&oldid=prev
Taifun den 9 oktober 2015 kl. 10.13
2015-10-09T10:13:53Z
<p></p>
<table class='diff diff-contentalign-left'>
<col class='diff-marker' />
<col class='diff-content' />
<col class='diff-marker' />
<col class='diff-content' />
<tr style='vertical-align: top;'>
<td colspan='2' style="background-color: white; color:black; text-align: center;">← Äldre version</td>
<td colspan='2' style="background-color: white; color:black; text-align: center;">Versionen från 9 oktober 2015 kl. 10.13</td>
</tr><tr><td colspan="2" class="diff-lineno">Rad 1:</td>
<td colspan="2" class="diff-lineno">Rad 1:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>::<math>\begin{align} \ln\,x                        & = 1 + \ln\,(x-1) \; & &\;| \; - \ln\,(x-1) \\</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>::<math>\begin{align} \ln\,x                        & = 1 + \ln\,(x-1) \; & &\;| \; - \ln\,(x-1) \\</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>                     \ln\,x - \ln\,(x-1)            & = 1 \; & &\;: \;\text{Logaritmlag 2 i VL}  \\</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>                     \ln\,x - \ln\,(x-1)            & = 1 <ins class="diffchange diffchange-inline">            </ins>\; & &\;: \;\text{Logaritmlag 2 i VL}  \\</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>                     \ln\,\left({x \over x-1}\right) & = 1 \; & &\;| \; e\,^{\cdot}                \\</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>                     \ln\,\left({x \over x-1}\right) & = 1 \; & &\;| \; e\,^{\cdot}                \\</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>                                       {x \over x-1} & = e \; & &\;| \; \cdot (x-1)                \\</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>                                       {x \over x-1} & = e \; & &\;| \; \cdot (x-1)                \\</div></td></tr>
<tr><td colspan="2" class="diff-lineno">Rad 6:</td>
<td colspan="2" class="diff-lineno">Rad 6:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>                                     {\color{Red} x} & = e \cdot {\color{Red} x} - e \;  & &\;| \; + e  \\</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>                                     {\color{Red} x} & = e \cdot {\color{Red} x} - e \;  & &\;| \; + e  \\</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>                                 {\color{Red} x} + e & = e \cdot {\color{Red} x}    \;  & &\;| \; - {\color{Red} x} \\</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>                                 {\color{Red} x} + e & = e \cdot {\color{Red} x}    \;  & &\;| \; - {\color{Red} x} \\</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>                                                   e & = e \cdot {\color{Red} x} - {\color{Red} x} \; & &: \;\text{Bryt ut} \; {\color{Red} x} \;\text{i HL } \\</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>                                                   e & = e \cdot {\color{Red} x} - {\color{Red} x} \; & &<ins class="diffchange diffchange-inline">\;</ins>: \;\text{Bryt ut} \; {\color{Red} x} \;\text{i HL } \\</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>                                                   e & = {\color{Red} x} \cdot (e - 1) \; & &\;| \; / \; (e-1) \\</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>                                                   e & = {\color{Red} x} \cdot (e - 1) \; & &\;| \; / \; (e-1) \\</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>                                       {e \over e-1} & = {\color{Red} x} \\</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>                                       {e \over e-1} & = {\color{Red} x} \\</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>                                     {\color{Red} x} & = {e \over e-1}  </div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>                                     {\color{Red} x} & = {e \over e-1}  </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>       \end{align}</math></div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>       \end{align}</math></div></td></tr>
</table>
Taifun
https://matte3c.mathonline.se/index.php?title=1.8_L%C3%B6sning_5a&diff=25111&oldid=prev
Taifun den 9 oktober 2015 kl. 10.13
2015-10-09T10:13:03Z
<p></p>
<table class='diff diff-contentalign-left'>
<col class='diff-marker' />
<col class='diff-content' />
<col class='diff-marker' />
<col class='diff-content' />
<tr style='vertical-align: top;'>
<td colspan='2' style="background-color: white; color:black; text-align: center;">← Äldre version</td>
<td colspan='2' style="background-color: white; color:black; text-align: center;">Versionen från 9 oktober 2015 kl. 10.13</td>
</tr><tr><td colspan="2" class="diff-lineno">Rad 1:</td>
<td colspan="2" class="diff-lineno">Rad 1:</td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>::<math>\begin{align} \ln\,x                        & = 1 + \ln\,(x-1) \; & & | \; - \ln\,(x-1) \\</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>::<math>\begin{align} \ln\,x                        & = 1 + \ln\,(x-1) \; & &<ins class="diffchange diffchange-inline">\;</ins>| \; - \ln\,(x-1) \\</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>                     \ln\,x - \ln\,(x-1)            & = 1 \; & &: \;\text{Logaritmlag 2 i VL}  \\</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>                     \ln\,x - \ln\,(x-1)            & = 1 \; & &<ins class="diffchange diffchange-inline">\;</ins>: \;\text{Logaritmlag 2 i VL}  \\</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>                     \ln\,\left({x \over x-1}\right) & = 1 \; & &\;| \; e\,^{\cdot}                \\</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>                     \ln\,\left({x \over x-1}\right) & = 1 \; & &\;| \; e\,^{\cdot}                \\</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>                                       {x \over x-1} & = e \; & &\;| \; \cdot (x-1)                \\</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>                                       {x \over x-1} & = e \; & &\;| \; \cdot (x-1)                \\</div></td></tr>
</table>
Taifun
https://matte3c.mathonline.se/index.php?title=1.8_L%C3%B6sning_5a&diff=25110&oldid=prev
Taifun den 9 oktober 2015 kl. 10.12
2015-10-09T10:12:12Z
<p></p>
<table class='diff diff-contentalign-left'>
<col class='diff-marker' />
<col class='diff-content' />
<col class='diff-marker' />
<col class='diff-content' />
<tr style='vertical-align: top;'>
<td colspan='2' style="background-color: white; color:black; text-align: center;">← Äldre version</td>
<td colspan='2' style="background-color: white; color:black; text-align: center;">Versionen från 9 oktober 2015 kl. 10.12</td>
</tr><tr><td colspan="2" class="diff-lineno">Rad 1:</td>
<td colspan="2" class="diff-lineno">Rad 1:</td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>::<math>\begin{align} \ln\,x                        & = 1 + \ln\,(x-1) \<del class="diffchange diffchange-inline">qquad\qquad\qquad </del>| \; - \ln\,(x-1) \\</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>::<math>\begin{align} \ln\,x                        & = 1 + \ln\,(x-1) \<ins class="diffchange diffchange-inline">; & & </ins>| \; - \ln\,(x-1) \\</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>                     \ln\,x - \ln\,(x-1)            & = 1 <del class="diffchange diffchange-inline">            </del>\<del class="diffchange diffchange-inline">qquad\qquad\qquad </del>: \;\text{Logaritmlag 2 i VL}  \\</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>                     \ln\,x - \ln\,(x-1)            & = 1 \<ins class="diffchange diffchange-inline">; & &</ins>: \;\text{Logaritmlag 2 i VL}  \\</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>                     \ln\,\left({x \over x-1}\right) & = 1 \; & &\;| \; e\,^{\cdot}                \\</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>                     \ln\,\left({x \over x-1}\right) & = 1 \; & &\;| \; e\,^{\cdot}                \\</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>                                       {x \over x-1} & = e \; & &\;| \; \cdot (x-1)                \\</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>                                       {x \over x-1} & = e \; & &\;| \; \cdot (x-1)                \\</div></td></tr>
</table>
Taifun
https://matte3c.mathonline.se/index.php?title=1.8_L%C3%B6sning_5a&diff=25109&oldid=prev
Taifun den 9 oktober 2015 kl. 10.11
2015-10-09T10:11:16Z
<p></p>
<table class='diff diff-contentalign-left'>
<col class='diff-marker' />
<col class='diff-content' />
<col class='diff-marker' />
<col class='diff-content' />
<tr style='vertical-align: top;'>
<td colspan='2' style="background-color: white; color:black; text-align: center;">← Äldre version</td>
<td colspan='2' style="background-color: white; color:black; text-align: center;">Versionen från 9 oktober 2015 kl. 10.11</td>
</tr><tr><td colspan="2" class="diff-lineno">Rad 1:</td>
<td colspan="2" class="diff-lineno">Rad 1:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>::<math>\begin{align} \ln\,x                        & = 1 + \ln\,(x-1) \qquad\qquad\qquad | \; - \ln\,(x-1) \\</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>::<math>\begin{align} \ln\,x                        & = 1 + \ln\,(x-1) \qquad\qquad\qquad | \; - \ln\,(x-1) \\</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>                     \ln\,x <del class="diffchange diffchange-inline">                        & = 1 + </del>\ln\,(x-1) \qquad\qquad\qquad <del class="diffchange diffchange-inline">| \; - \ln\,(x-1) \\</del></div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>                     \ln\,x <ins class="diffchange diffchange-inline">- </ins>\ln\,(x-1) <ins class="diffchange diffchange-inline">            & = 1              </ins>\qquad\qquad\qquad : \;\text{Logaritmlag 2 i VL} <ins class="diffchange diffchange-inline"> </ins>\\</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">                    \ln\,x - \ln\,(x-1)            & = 1 \; & &</del>: \;\text{Logaritmlag 2 i VL} <del class="diffchange diffchange-inline">    </del>\\</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>                     \ln\,\left({x \over x-1}\right) & = 1 \; & &\;| \; e\,^{\cdot}                \\</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>                     \ln\,\left({x \over x-1}\right) & = 1 \; & &\;| \; e\,^{\cdot}                \\</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>                                       {x \over x-1} & = e \; & &\;| \; \cdot (x-1)                \\</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>                                       {x \over x-1} & = e \; & &\;| \; \cdot (x-1)                \\</div></td></tr>
</table>
Taifun