http://wiki.sommarmatte.se/wikis/2009/bridgecourse1-ImperialCollege/index.php?action=history&feed=atom&title=Solution_3.3%3A3c 2026-04-08T10:10:22Z Revision history for this page on the wiki MediaWiki 1.11.1 http://wiki.sommarmatte.se/wikis/2009/bridgecourse1-ImperialCollege/index.php?title=Solution_3.3:3c&diff=5746&oldid=prev 2008-10-02T06:33:42Z

<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 06:33, 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: #ffa; color:black; font-size: smaller;"><div>First, we rewrite the number </div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>First, we rewrite the number 0.125 as a fraction which we also simplify</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;</del>0.<del style="color: red; font-weight: bold; text-decoration: none;">\text{</del>125 <del style="color: red; font-weight: bold; text-decoration: none;">}&lt;/math&gt;</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>as a fraction which we also simplify<del style="color: red; font-weight: bold; text-decoration: none;">:</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: #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;0\textrm{.}125 = \frac{125}{1000} = \frac{5\cdot 25}{10^3} = \frac{5\cdot 5\cdot 5}{(2\cdot 5)^3} = \frac{1}{2^3} = 2^{-3}\,\textrm{.}&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><del style="color: red; font-weight: bold; text-decoration: none;">&lt;math&gt;</del>0.<del style="color: red; font-weight: bold; text-decoration: none;">\text{</del>125 <del style="color: red; font-weight: bold; text-decoration: none;">}=\frac{\text{125 }}{1000}=\frac{5\centerdot 25}{10^{3}}=\frac{5\centerdot 5\centerdot 5}{\left( 2\centerdot 5 \right)^{3}}=\frac{1}{2^{3}}=</del>2<del style="color: red; font-weight: bold; text-decoration: none;">^{-3}&lt;/math&gt;</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;">Because </ins>0.125 <ins style="color: red; font-weight: bold; text-decoration: none;">was expressed as a power of </ins>2<ins style="color: red; font-weight: bold; text-decoration: none;">, the logarithm can be calculated in full</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;\<ins style="color: red; font-weight: bold; text-decoration: none;">log_2 </ins>0\<ins style="color: red; font-weight: bold; text-decoration: none;">textrm</ins>{<ins style="color: red; font-weight: bold; text-decoration: none;">.}</ins>125 = \<ins style="color: red; font-weight: bold; text-decoration: none;">log_2 </ins>2^{-3} = (-3)\<ins style="color: red; font-weight: bold; text-decoration: none;">cdot</ins>\<ins style="color: red; font-weight: bold; text-decoration: none;">log_2 </ins>2 = (-3)\<ins style="color: red; font-weight: bold; text-decoration: none;">cdot </ins>1 = -3<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;">Because </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;0.\text</del>{<del style="color: red; font-weight: bold; text-decoration: none;">125 }&lt;/math&gt;</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;">was expressed as a power of </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;\text</del>{<del style="color: red; font-weight: bold; text-decoration: none;">2}&lt;/</del>math<del style="color: red; font-weight: bold; text-decoration: none;">&gt;, the logarithm can be calculated in full:</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;\<del style="color: red; font-weight: bold; text-decoration: none;">log _{2}</del>0<del style="color: red; font-weight: bold; text-decoration: none;">.</del>\<del style="color: red; font-weight: bold; text-decoration: none;">text</del>{125 <del style="color: red; font-weight: bold; text-decoration: none;">}</del>=\<del style="color: red; font-weight: bold; text-decoration: none;">log _{2}</del>2^{-3}=<del style="color: red; font-weight: bold; text-decoration: none;">\left</del>( -3 <del style="color: red; font-weight: bold; text-decoration: none;">\right</del>)\<del style="color: red; font-weight: bold; text-decoration: none;">centerdot </del>\<del style="color: red; font-weight: bold; text-decoration: none;">log _{2}</del>2=<del style="color: red; font-weight: bold; text-decoration: none;">\left</del>( -3 <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=-3&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_3.3:3c&diff=5492&oldid=prev 2008-09-25T14:13:09Z

<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 14:13, 25 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;">First, we rewrite the number </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_3c</del>.<del style="color: red; font-weight: bold; text-decoration: none;">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><ins style="color: red; font-weight: bold; text-decoration: none;">&lt;math&gt;0.\text</ins>{<ins style="color: red; font-weight: bold; text-decoration: none;">125 }&lt;/math&gt;</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;">NAVCONTENT_STOP</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;">as a fraction which we also simplify:</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;0.\text</ins>{<ins style="color: red; font-weight: bold; text-decoration: none;">125 </ins>}<ins style="color: red; font-weight: bold; text-decoration: none;">=\frac{\text{125 </ins>}<ins style="color: red; font-weight: bold; text-decoration: none;">}{1000}=\frac{5\centerdot 25}{10^{3}}=\frac{5\centerdot 5\centerdot 5}{\left( 2\centerdot 5 \right)^{3}}=\frac{1}{2^{3}}=2^{-3}&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;">Because </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;">0</ins>.<ins style="color: red; font-weight: bold; text-decoration: none;">\text{125 }</ins>&lt;/<ins style="color: red; font-weight: bold; text-decoration: none;">math</ins>&gt;</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;">was expressed as a power of </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><ins style="color: red; font-weight: bold; text-decoration: none;">&lt;math&gt;\text</ins>{<ins style="color: red; font-weight: bold; text-decoration: none;">2}&lt;/math&gt;, the logarithm can be calculated in full:</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;\log _</ins>{<ins style="color: red; font-weight: bold; text-decoration: none;">2</ins>}<ins style="color: red; font-weight: bold; text-decoration: none;">0.\text{125 </ins>}<ins style="color: red; font-weight: bold; text-decoration: none;">=\log _{2}2^{-3}=\left( -3 \right)\centerdot \log _{2}2=\left( -3 \right)\centerdot 1=-3&lt;/math&gt;</ins></div></td></tr> </table>

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<p><a href="/wikis/2009/bridgecourse1-ImperialCollege/index.php?title=L%C3%B6sning_3.3:3c&amp;action=edit" class="new" title="Lösning 3.3:3c">Lösning 3.3:3c</a> moved to <a href="/wikis/2009/bridgecourse1-ImperialCollege/index.php/Solution_3.3:3c" title="Solution 3.3:3c">Solution 3.3:3c</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 09:24, 9 September 2008</td> </tr> </table>

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