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1.8 Lösning 3a - Versionshistorik
2026-06-26T14:50:49Z
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Taifun den 11 april 2011 kl. 03.36
2011-04-11T03:36:42Z
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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 11 april 2011 kl. 03.36</td>
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<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;"></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;"></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}  e\,^0 & = 1      \quad  & &\,| \;  \ln\,(\;\;)                \\</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}  e\,^0 & = 1      \quad  & &\,| \;  \ln\,(\;\;)                \\</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\,(e^0) & = \ln\,1 \quad  & &: \;\text{Inversegenskapen av ln och e<del class="diffchange diffchange-inline">} </del>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\,(e^0) & = \ln\,1 \quad  & &: \;\text{Inversegenskapen av ln och e i VL<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>                           0  & = \ln\,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>                           0  & = \ln\,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>                       \ln\,1 & = 0  </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\,1 & = 0  </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
https://minidemo.mathonline.se/index.php?title=1.8_L%C3%B6sning_3a&diff=4082&oldid=prev
Taifun den 11 april 2011 kl. 03.36
2011-04-11T03:36:19Z
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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 11 april 2011 kl. 03.36</td>
</tr><tr><td colspan="2" class="diff-lineno">Rad 2:</td>
<td colspan="2" class="diff-lineno">Rad 2:</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;"></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;"></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}  e\,^0 & = 1      \quad  & &\,| \;  \ln\,(\;\;)                \\</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}  e\,^0 & = 1      \quad  & &\,| \;  \ln\,(\;\;)                \\</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\,(e^0) & = \ln\,1 \quad  & &: \;\text{Inversegenskapen av ln och e} \\</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\,(e^0) & = \ln\,1 \quad  & &: \;\text{Inversegenskapen av ln och e} <ins class="diffchange diffchange-inline">i VL</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>                           0  & = \ln\,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>                           0  & = \ln\,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>                       \ln\,1 & = 0  </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\,1 & = 0  </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
https://minidemo.mathonline.se/index.php?title=1.8_L%C3%B6sning_3a&diff=3727&oldid=prev
Taifun den 21 mars 2011 kl. 03.49
2011-03-21T03:49:32Z
<p></p>
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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 21 mars 2011 kl. 03.49</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>För att skriva i logaritmform logaritmerar vi båda leden:</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>För att skriva i logaritmform logaritmerar vi båda leden <ins class="diffchange diffchange-inline">med den naturliga logaritmen</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;"></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;"></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}  <del class="diffchange diffchange-inline">2</del>^<del class="diffchange diffchange-inline">x </del>& = <del class="diffchange diffchange-inline">35      </del>\<del class="diffchange diffchange-inline">qquad </del> & &\,| \;  \<del class="diffchange diffchange-inline">lg</del>\,(\;\;) <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>:::<math>\begin{align}  <ins class="diffchange diffchange-inline">e\,</ins>^<ins class="diffchange diffchange-inline">0 </ins>& = <ins class="diffchange diffchange-inline">1      </ins>\<ins class="diffchange diffchange-inline">quad </ins> & &\,| \;  \<ins class="diffchange diffchange-inline">ln</ins>\,(\;\;) <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">                  </del>\<del class="diffchange diffchange-inline">lg</del>\,(<del class="diffchange diffchange-inline">2</del>^<del class="diffchange diffchange-inline">x</del>) & = \<del class="diffchange diffchange-inline">lg</del>\,<del class="diffchange diffchange-inline">35 </del>\<del class="diffchange diffchange-inline">qquad </del> & &: \;\text{<del class="diffchange diffchange-inline">3:</del>e <del class="diffchange diffchange-inline">logaritmlag i VL</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><ins class="diffchange diffchange-inline">                  </ins>\<ins class="diffchange diffchange-inline">ln</ins>\,(<ins class="diffchange diffchange-inline">e</ins>^<ins class="diffchange diffchange-inline">0</ins>) & = \<ins class="diffchange diffchange-inline">ln</ins>\,<ins class="diffchange diffchange-inline">1 </ins>\<ins class="diffchange diffchange-inline">quad </ins> & &: \;\text{<ins class="diffchange diffchange-inline">Inversegenskapen av ln och </ins>e} \\</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">              x \cdot \lg\,2 </del>& = \<del class="diffchange diffchange-inline">lg</del>\,<del class="diffchange diffchange-inline">35 \qquad  & &\,| \; / \lg\,2                  </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><ins class="diffchange diffchange-inline">                          0  </ins>& = \<ins class="diffchange diffchange-inline">ln</ins>\,<ins class="diffchange diffchange-inline">1                                                </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">                          x & = {</del>\<del class="diffchange diffchange-inline">lg</del>\,<del class="diffchange diffchange-inline">35 \over \lg\,2}                              \\</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><ins class="diffchange diffchange-inline">                      </ins>\<ins class="diffchange diffchange-inline">ln</ins>\,<ins class="diffchange diffchange-inline">1 </ins>& = <ins class="diffchange diffchange-inline">0 </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">                          x </del>& = <del class="diffchange diffchange-inline">5,129283</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>       \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
https://minidemo.mathonline.se/index.php?title=1.8_L%C3%B6sning_3a&diff=3726&oldid=prev
Taifun: Created page with "För att skriva i logaritmform logaritmerar vi båda leden: :::<math>\begin{align} 2^x & = 35 \qquad & &\,| \; \lg\,(\;\;) \\ \lg\,(2^x) &..."
2011-03-21T03:42:40Z
<p>Created page with "För att skriva i logaritmform logaritmerar vi båda leden: :::<math>\begin{align} 2^x & = 35 \qquad & &\,| \; \lg\,(\;\;) \\ \lg\,(2^x) &..."</p>
<p><b>Ny sida</b></p><div>För att skriva i logaritmform logaritmerar vi båda leden:<br />
<br />
:::<math>\begin{align} 2^x & = 35 \qquad & &\,| \; \lg\,(\;\;) \\<br />
\lg\,(2^x) & = \lg\,35 \qquad & &: \;\text{3:e logaritmlag i VL} \\<br />
x \cdot \lg\,2 & = \lg\,35 \qquad & &\,| \; / \lg\,2 \\<br />
x & = {\lg\,35 \over \lg\,2} \\<br />
x & = 5,129283<br />
\end{align}</math></div>
Taifun