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1.7 Lösning 5b - Versionshistorik
2026-04-12T06:47:44Z
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Taifun den 8 juli 2015 kl. 15.15
2015-07-08T15:15:03Z
<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 8 juli 2015 kl. 15.15</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><del class="diffchange diffchange-inline">\begin{align}        2 \cdot 3^x & = </del>4 <del class="diffchange diffchange-inline">\cdot 5^x            \; & &\;| \;\lg</del>\,<del class="diffchange diffchange-inline">(</del>\,<del class="diffchange diffchange-inline">\cdot</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><ins class="diffchange diffchange-inline">:</ins><math> 4\,<ins class="diffchange diffchange-inline">800</ins>\,<ins class="diffchange diffchange-inline">000</ins>\,<ins class="diffchange diffchange-inline">000  </ins>\, = \, <ins class="diffchange diffchange-inline">48 </ins>\cdot <ins class="diffchange diffchange-inline">100</ins>\,<ins class="diffchange diffchange-inline">000</ins>\,<ins class="diffchange diffchange-inline">000 </ins>\, = \, <ins class="diffchange diffchange-inline">48 </ins>\<ins class="diffchange diffchange-inline">cdot 10</ins>\,^<ins class="diffchange diffchange-inline">8 </ins>\, = \, 4,<ins class="diffchange diffchange-inline">8 </ins>\cdot <ins class="diffchange diffchange-inline">10</ins>\,<ins class="diffchange diffchange-inline">^9 </ins></math></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">                    \lg</del>\,<del class="diffchange diffchange-inline">(2 \cdot 3^x) & </del>= <del class="diffchange diffchange-inline">\lg</del>\,<del class="diffchange diffchange-inline">(4 </del>\cdot <del class="diffchange diffchange-inline">5^x)    \; & &: \;\text{Logaritmlag 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></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">                  \lg</del>\,<del class="diffchange diffchange-inline">2 + \lg</del>\,<del class="diffchange diffchange-inline">(3</del>\,<del class="diffchange diffchange-inline">^x) & </del>= <del class="diffchange diffchange-inline">\lg</del>\,<del class="diffchange diffchange-inline">4 + </del>\<del class="diffchange diffchange-inline">lg\,(5</del>\,^<del class="diffchange diffchange-inline">x)  \; & &: \;\text{Logaritmlag 3}\\</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="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">                  \lg</del>\,<del class="diffchange diffchange-inline">2 + x\cdot\lg\,3 & </del>= <del class="diffchange diffchange-inline">\lg</del>\,4 <del class="diffchange diffchange-inline">+ x\cdot\lg\</del>,<del class="diffchange diffchange-inline">5  \; & &\;| \; - x</del>\cdot<del class="diffchange diffchange-inline">\lg</del>\,<del class="diffchange diffchange-inline">5 -\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></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\,3 - x\cdot\lg\,5 & = \lg\,4 - \lg\,2      \; & &: \;\text{Bryt ut x 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></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\,3 - \lg\,5) & = \lg\,4 - \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></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  & = {\lg\,4 - \lg\,2 \over \lg\,3 - \lg\,5}</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="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">      \end{align}</del></math></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>
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Taifun
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Taifun den 12 april 2011 kl. 22.53
2011-04-12T22:53:57Z
<p></p>
<table class='diff diff-contentalign-left'>
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<col class='diff-marker' />
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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 12 april 2011 kl. 22.53</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;"><div>                     \lg\,(2 \cdot 3^x) & = \lg\,(4 \cdot 5^x)    \; & &: \;\text{Logaritmlag 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>                     \lg\,(2 \cdot 3^x) & = \lg\,(4 \cdot 5^x)    \; & &: \;\text{Logaritmlag 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>                   \lg\,2 + \lg\,(3\,^x) & = \lg\,4 + \lg\,(5\,^x)  \; & &: \;\text{Logaritmlag 3}\\</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>                   \lg\,2 + \lg\,(3\,^x) & = \lg\,4 + \lg\,(5\,^x)  \; & &: \;\text{Logaritmlag 3}\\</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>                   \lg\,2 + x\cdot\lg\,3 & = \lg\,4 + x\cdot\lg\,5  \; & &\;| \; - x\cdot\lg\,5 -\lg\,<del class="diffchange diffchange-inline">3 </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>                   \lg\,2 + x\cdot\lg\,3 & = \lg\,4 + x\cdot\lg\,5  \; & &\;| \; - x\cdot\lg\,5 -\lg\,<ins class="diffchange diffchange-inline">2 </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>             x\cdot\lg\,3 - x\cdot\lg\,5 & = \lg\,4 - \lg\,2      \; & &: \;\text{Bryt ut x i VL}\\   </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\cdot\lg\,3 - x\cdot\lg\,5 & = \lg\,4 - \lg\,2      \; & &: \;\text{Bryt ut x 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>                 x\cdot(\lg\,3 - \lg\,5) & = \lg\,4 - \lg\,2  \\   </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\cdot(\lg\,3 - \lg\,5) & = \lg\,4 - \lg\,2  \\   </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  & = {\lg\,4 - \lg\,2 \over \lg\,3 - \lg\,5}</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  & = {\lg\,4 - \lg\,2 \over \lg\,3 - \lg\,5}</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://minidemo.mathonline.se/index.php?title=1.7_L%C3%B6sning_5b&diff=4119&oldid=prev
Taifun den 12 april 2011 kl. 22.53
2011-04-12T22:53:14Z
<p></p>
<table class='diff diff-contentalign-left'>
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<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 12 april 2011 kl. 22.53</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}        2 \cdot 3^x & = 4 \cdot 5^x            \; & &\;| \;\lg\,(\,\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><math>\begin{align}        2 \cdot 3^x & = 4 \cdot 5^x            \; & &\;| \;\lg\,(\,\cdot\,)  \\</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>                     \lg\,(2 \cdot 3^x) & = \lg\,(4 \cdot 5^x)    \; & &: \;\text{Logaritmlag 1 <del class="diffchange diffchange-inline">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>                     \lg\,(2 \cdot 3^x) & = \lg\,(4 \cdot 5^x)    \; & &: \;\text{Logaritmlag 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>                   \lg\,2 + \lg\,(3\,^x) & = \lg\,4 + \lg\,(5\,^x)  \; & &: \;\text{Logaritmlag 3 <del class="diffchange diffchange-inline">i VL + 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>                   \lg\,2 + \lg\,(3\,^x) & = \lg\,4 + \lg\,(5\,^x)  \; & &: \;\text{Logaritmlag 3}\\</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>                   \lg\,2 + x\cdot\lg\,3 & = \lg\,4 + x\cdot\lg\,5  \; & &\;| \; - x\cdot\lg\,5 -\lg\,3 \\</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>                   \lg\,2 + x\cdot\lg\,3 & = \lg\,4 + x\cdot\lg\,5  \; & &\;| \; - x\cdot\lg\,5 -\lg\,3 \\</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\cdot\lg\,3 - x\cdot\lg\,5 & = \lg\,4 - \lg\,2      \; & &: \;\text{Bryt ut x i VL}\\   </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\cdot\lg\,3 - x\cdot\lg\,5 & = \lg\,4 - \lg\,2      \; & &: \;\text{Bryt ut x i VL}\\   </div></td></tr>
</table>
Taifun
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Taifun den 12 april 2011 kl. 22.49
2011-04-12T22:49:08Z
<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 12 april 2011 kl. 22.49</td>
</tr><tr><td colspan="2" class="diff-lineno">Rad 4:</td>
<td colspan="2" class="diff-lineno">Rad 4:</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>                   \lg\,2 + x\cdot\lg\,3 & = \lg\,4 + x\cdot\lg\,5  \; & &\;| \; - x\cdot\lg\,5 -\lg\,3 \\</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>                   \lg\,2 + x\cdot\lg\,3 & = \lg\,4 + x\cdot\lg\,5  \; & &\;| \; - x\cdot\lg\,5 -\lg\,3 \\</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\cdot\lg\,3 - x\cdot\lg\,5 & = \lg\,4 - \lg\,2      \; & &: \;\text{Bryt ut x i VL}\\   </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\cdot\lg\,3 - x\cdot\lg\,5 & = \lg\,4 - \lg\,2      \; & &: \;\text{Bryt ut x 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>                 x\cdot(\lg\,<del class="diffchange diffchange-inline">6 </del>- \lg\,<del class="diffchange diffchange-inline">7</del>) & = -\lg\,<del class="diffchange diffchange-inline">5 </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\cdot(\lg\,<ins class="diffchange diffchange-inline">3 </ins>- \lg\,<ins class="diffchange diffchange-inline">5</ins>) & = <ins class="diffchange diffchange-inline">\lg\,4 </ins>- \lg\,<ins class="diffchange diffchange-inline">2 </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  & = {-\lg\,<del class="diffchange diffchange-inline">5 </del>\over \lg\,<del class="diffchange diffchange-inline">6 </del>- \lg\,<del class="diffchange diffchange-inline">7</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  & = {<ins class="diffchange diffchange-inline">\lg\,4 </ins>- \lg\,<ins class="diffchange diffchange-inline">2 </ins>\over \lg\,<ins class="diffchange diffchange-inline">3 </ins>- \lg\,<ins class="diffchange diffchange-inline">5</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>       \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=1.7_L%C3%B6sning_5b&diff=4116&oldid=prev
Taifun den 12 april 2011 kl. 22.47
2011-04-12T22:47:11Z
<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 12 april 2011 kl. 22.47</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} <del class="diffchange diffchange-inline">      5 </del>\cdot <del class="diffchange diffchange-inline">6\,</del>^x & = <del class="diffchange diffchange-inline">7</del>\<del class="diffchange diffchange-inline">,</del>^x <del class="diffchange diffchange-inline">        </del>\; & &\;| \;\lg\,(\,\cdot\,)  \\</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">        2 </ins>\cdot <ins class="diffchange diffchange-inline">3</ins>^x & = <ins class="diffchange diffchange-inline">4 </ins>\<ins class="diffchange diffchange-inline">cdot 5</ins>^x <ins class="diffchange diffchange-inline">          </ins>\; & &\;| \;\lg\,(\,\cdot\,)  \\</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>\lg\,(<del class="diffchange diffchange-inline">5 </del>\cdot <del class="diffchange diffchange-inline">6\,</del>^x) & = \lg\,(<del class="diffchange diffchange-inline">7</del>\<del class="diffchange diffchange-inline">,</del>^x) <del class="diffchange diffchange-inline"> </del>\; & &: \;\text{Logaritmlag 1 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><ins class="diffchange diffchange-inline">                    </ins>\lg\,(<ins class="diffchange diffchange-inline">2 </ins>\cdot <ins class="diffchange diffchange-inline">3</ins>^x) & = \lg\,(<ins class="diffchange diffchange-inline">4 </ins>\<ins class="diffchange diffchange-inline">cdot 5</ins>^x) <ins class="diffchange diffchange-inline">    </ins>\; & &: \;\text{Logaritmlag 1 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>                   \lg\,<del class="diffchange diffchange-inline">5 </del>+ \lg\,(<del class="diffchange diffchange-inline">6</del>\,^x) & = \lg\,(<del class="diffchange diffchange-inline">7</del>\,^x)  \; & &: \;\text{Logaritmlag 3 i VL + 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>                   \lg\,<ins class="diffchange diffchange-inline">2 </ins>+ \lg\,(<ins class="diffchange diffchange-inline">3</ins>\,^x) & = <ins class="diffchange diffchange-inline">\lg\,4 + </ins>\lg\,(<ins class="diffchange diffchange-inline">5</ins>\,^x)  \; & &: \;\text{Logaritmlag 3 i VL + 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>                   \lg\,<del class="diffchange diffchange-inline">5 </del>+ x\cdot\lg\,<del class="diffchange diffchange-inline">6 </del>& = x\cdot\lg\,<del class="diffchange diffchange-inline">7 </del> \; & &\;| \; - x\cdot\lg\,<del class="diffchange diffchange-inline">7 </del>-\lg\,<del class="diffchange diffchange-inline">5 </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>                   \lg\,<ins class="diffchange diffchange-inline">2 </ins>+ x\cdot\lg\,<ins class="diffchange diffchange-inline">3 </ins>& = <ins class="diffchange diffchange-inline">\lg\,4 + </ins>x\cdot\lg\,<ins class="diffchange diffchange-inline">5 </ins> \; & &\;| \; - x\cdot\lg\,<ins class="diffchange diffchange-inline">5 </ins>-\lg\,<ins class="diffchange diffchange-inline">3 </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\cdot\lg\,<del class="diffchange diffchange-inline">6 </del>- x\cdot\lg\,<del class="diffchange diffchange-inline">7 </del>& = -\lg\,<del class="diffchange diffchange-inline">5 </del>      \; & &: \;\text{Bryt ut x 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>             x\cdot\lg\,<ins class="diffchange diffchange-inline">3 </ins>- x\cdot\lg\,<ins class="diffchange diffchange-inline">5 </ins>& = <ins class="diffchange diffchange-inline">\lg\,4 </ins>- \lg\,<ins class="diffchange diffchange-inline">2 </ins>      \; & &: \;\text{Bryt ut x 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>                 x\cdot(\lg\,6 - \lg\,7) & = -\lg\,5  \\   </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\cdot(\lg\,6 - \lg\,7) & = -\lg\,5  \\   </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  & = {-\lg\,5 \over \lg\,6 - \lg\,7}</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  & = {-\lg\,5 \over \lg\,6 - \lg\,7}</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=1.7_L%C3%B6sning_5b&diff=4115&oldid=prev
Taifun: Created page with "<math>\begin{align} 5 \cdot 6\,^x & = 7\,^x \; & &\;| \;\lg\,(\,\cdot\,) \\ \lg\,(5 \cdot 6\,^x) & = \lg\,(7\,^x) \; & &: \;\text{Logaritmlag ..."
2011-04-12T22:41:28Z
<p>Created page with "<math>\begin{align} 5 \cdot 6\,^x & = 7\,^x \; & &\;| \;\lg\,(\,\cdot\,) \\ \lg\,(5 \cdot 6\,^x) & = \lg\,(7\,^x) \; & &: \;\text{Logaritmlag ..."</p>
<p><b>Ny sida</b></p><div><math>\begin{align} 5 \cdot 6\,^x & = 7\,^x \; & &\;| \;\lg\,(\,\cdot\,) \\<br />
\lg\,(5 \cdot 6\,^x) & = \lg\,(7\,^x) \; & &: \;\text{Logaritmlag 1 i VL}\\<br />
\lg\,5 + \lg\,(6\,^x) & = \lg\,(7\,^x) \; & &: \;\text{Logaritmlag 3 i VL + HL}\\<br />
\lg\,5 + x\cdot\lg\,6 & = x\cdot\lg\,7 \; & &\;| \; - x\cdot\lg\,7 -\lg\,5 \\<br />
x\cdot\lg\,6 - x\cdot\lg\,7 & = -\lg\,5 \; & &: \;\text{Bryt ut x i VL}\\ <br />
x\cdot(\lg\,6 - \lg\,7) & = -\lg\,5 \\ <br />
x & = {-\lg\,5 \over \lg\,6 - \lg\,7}<br />
\end{align}</math></div>
Taifun