http://wiki.sommarmatte.se/wikis/2009/bridgecourse1-ImperialCollege/index.php?action=history&feed=atom&title=Solution_3.3%3A5e 2026-04-08T07:58:11Z Revision history for this page on the wiki MediaWiki 1.11.1 http://wiki.sommarmatte.se/wikis/2009/bridgecourse1-ImperialCollege/index.php?title=Solution_3.3:5e&diff=5759&oldid=prev 2008-10-02T07:33:15Z

<p></p> <table style="background-color: white; color:black;"> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr> <td colspan='2' style="background-color: white; color:black;">←Older revision</td> <td colspan='2' style="background-color: white; color:black;">Revision as of 07:33, 2 October 2008</td> </tr> <tr><td colspan="2" class="diff-lineno">Line 1:</td> <td colspan="2" class="diff-lineno">Line 1:</td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The argument of ln can be written as</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The argument of ln can be written as</div></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>{{Displayed math||&lt;math&gt;\frac{1}{e^{2}} = e^{-2}&lt;/math&gt;}}</div></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>&lt;math&gt;\<del style="color: red; font-weight: bold; text-decoration: none;">frac{1}{e</del>^{<del style="color: red; font-weight: bold; text-decoration: none;">2}</del>}=<del style="color: red; font-weight: bold; text-decoration: none;">e^{-2}</del>&lt;/math&gt;</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">and with the logarithm law, </ins>&lt;math&gt;\<ins style="color: red; font-weight: bold; text-decoration: none;">ln a</ins>^{<ins style="color: red; font-weight: bold; text-decoration: none;">b</ins>} = <ins style="color: red; font-weight: bold; text-decoration: none;">b\ln a</ins>&lt;/math&gt;<ins style="color: red; font-weight: bold; text-decoration: none;">, we obtain</ins></div></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>&#160;</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>{<ins style="color: red; font-weight: bold; text-decoration: none;">{Displayed </ins>math<ins style="color: red; font-weight: bold; text-decoration: none;">||</ins>&lt;math&gt;\ln \frac{1}{e^{2}} = \ln e^{-2} = (-2)\<ins style="color: red; font-weight: bold; text-decoration: none;">cdot</ins>\ln e = (-2)\<ins style="color: red; font-weight: bold; text-decoration: none;">cdot </ins>1 = -2<ins style="color: red; font-weight: bold; text-decoration: none;">\,\textrm{.}</ins>&lt;/math&gt;<ins style="color: red; font-weight: bold; text-decoration: none;">}}</ins></div></td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">and with the logarithm law, </del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">&lt;math&gt;\lg a^</del>{<del style="color: red; font-weight: bold; text-decoration: none;">b}=b\lg a&lt;/</del>math<del style="color: red; font-weight: bold; text-decoration: none;">&gt;, we obtain</del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>&#160;</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>&#160;</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>&lt;math&gt;\ln \frac{1}{e^{2}}=\ln e^{-2}=<del style="color: red; font-weight: bold; text-decoration: none;">\left</del>( -2 <del style="color: red; font-weight: bold; text-decoration: none;">\right</del>)\<del style="color: red; font-weight: bold; text-decoration: none;">centerdot </del>\ln e=<del style="color: red; font-weight: bold; text-decoration: none;">\left</del>( -2 <del style="color: red; font-weight: bold; text-decoration: none;">\right</del>)\<del style="color: red; font-weight: bold; text-decoration: none;">centerdot </del>1=-2&lt;/math&gt;</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr> </table>

Tek http://wiki.sommarmatte.se/wikis/2009/bridgecourse1-ImperialCollege/index.php?title=Solution_3.3:5e&diff=5513&oldid=prev 2008-09-26T08:45:52Z

<p></p> <table style="background-color: white; color:black;"> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr> <td colspan='2' style="background-color: white; color:black;">←Older revision</td> <td colspan='2' style="background-color: white; color:black;">Revision as of 08:45, 26 September 2008</td> </tr> <tr><td colspan="2" class="diff-lineno">Line 1:</td> <td colspan="2" class="diff-lineno">Line 1:</td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>{{<del style="color: red; font-weight: bold; text-decoration: none;">NAVCONTENT_START</del>}}</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">The argument of ln can be written as</ins></div></td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>&lt;<del style="color: red; font-weight: bold; text-decoration: none;">center</del>&gt; <del style="color: red; font-weight: bold; text-decoration: none;">[[Image:3_3_5e.gif]] </del>&lt;/<del style="color: red; font-weight: bold; text-decoration: none;">center</del>&gt;</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>&#160;</div></td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>{{<del style="color: red; font-weight: bold; text-decoration: none;">NAVCONTENT_STOP</del>}}</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>&#160;</div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">&lt;math&gt;\frac</ins>{<ins style="color: red; font-weight: bold; text-decoration: none;">1}</ins>{<ins style="color: red; font-weight: bold; text-decoration: none;">e^{2</ins>}}<ins style="color: red; font-weight: bold; text-decoration: none;">=e^{-2}&lt;/math&gt;</ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>&#160;</div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>&#160;</div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">and with the logarithm law, </ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>&lt;<ins style="color: red; font-weight: bold; text-decoration: none;">math</ins>&gt;<ins style="color: red; font-weight: bold; text-decoration: none;">\lg a^{b}=b\lg a</ins>&lt;/<ins style="color: red; font-weight: bold; text-decoration: none;">math</ins>&gt;<ins style="color: red; font-weight: bold; text-decoration: none;">, we obtain</ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>&#160;</div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>&#160;</div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">&lt;math&gt;\ln \frac</ins>{<ins style="color: red; font-weight: bold; text-decoration: none;">1}{e^</ins>{<ins style="color: red; font-weight: bold; text-decoration: none;">2</ins>}}<ins style="color: red; font-weight: bold; text-decoration: none;">=\ln e^{-2}=\left( -2 \right)\centerdot \ln e=\left( -2 \right)\centerdot 1=-2&lt;/math&gt;</ins></div></td></tr> </table>

Ian http://wiki.sommarmatte.se/wikis/2009/bridgecourse1-ImperialCollege/index.php?title=Solution_3.3:5e&diff=3624&oldid=prev 2008-09-09T09:28:23Z

<p><a href="/wikis/2009/bridgecourse1-ImperialCollege/index.php?title=L%C3%B6sning_3.3:5e&amp;action=edit" class="new" title="Lösning 3.3:5e">Lösning 3.3:5e</a> moved to <a href="/wikis/2009/bridgecourse1-ImperialCollege/index.php/Solution_3.3:5e" title="Solution 3.3:5e">Solution 3.3:5e</a>: Robot: moved page</p> <table style="background-color: white; color:black;"> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr> <td colspan='2' style="background-color: white; color:black;">←Older revision</td> <td colspan='2' style="background-color: white; color:black;">Revision as of 09:28, 9 September 2008</td> </tr> </table>

Tekbot http://wiki.sommarmatte.se/wikis/2009/bridgecourse1-ImperialCollege/index.php?title=Solution_3.3:5e&diff=2374&oldid=prev 2008-08-21T07:01:19Z

<p>Robot: Automated text replacement (-[[Bild: +[[Image:)</p> <table style="background-color: white; color:black;"> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr> <td colspan='2' style="background-color: white; color:black;">←Older revision</td> <td colspan='2' style="background-color: white; color:black;">Revision as of 07:01, 21 August 2008</td> </tr> <tr><td colspan="2" class="diff-lineno">Line 1:</td> <td colspan="2" class="diff-lineno">Line 1:</td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>{{NAVCONTENT_START}}</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>{{NAVCONTENT_START}}</div></td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>&lt;center&gt; [[<del style="color: red; font-weight: bold; text-decoration: none;">Bild</del>:3_3_5e.gif]] &lt;/center&gt;</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>&lt;center&gt; [[<ins style="color: red; font-weight: bold; text-decoration: none;">Image</ins>:3_3_5e.gif]] &lt;/center&gt;</div></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>{{NAVCONTENT_STOP}}</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>{{NAVCONTENT_STOP}}</div></td></tr> </table>

Tekbot http://wiki.sommarmatte.se/wikis/2009/bridgecourse1-ImperialCollege/index.php?title=Solution_3.3:5e&diff=1057&oldid=prev 2008-04-02T09:53:57Z

<p>Ny sida: {{NAVCONTENT_START}} &lt;center&gt; <a href="/wikis/2009/bridgecourse1-ImperialCollege/index.php?title=Bild:3_3_5e.gif&amp;action=edit" class="new" title="Bild:3 3 5e.gif">Bild:3_3_5e.gif</a> &lt;/center&gt; {{NAVCONTENT_STOP}}</p> <p><b>New page</b></p><div>{{NAVCONTENT_START}}<br /> &lt;center&gt; [[Bild:3_3_5e.gif]] &lt;/center&gt;<br /> {{NAVCONTENT_STOP}}</div>

Oskar