https://artofproblemsolving.com/wiki/index.php?title=1991_AHSME_Problems/Problem_24&feed=atom&action=history
1991 AHSME Problems/Problem 24 - Revision history
2024-03-28T14:29:06Z
Revision history for this page on the wiki
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Hapaxoromenon: Added a solution with explanation
2018-02-23T21:47:50Z
<p>Added a solution with explanation</p>
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<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Revision as of 21:47, 23 February 2018</td>
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<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== Solution ==</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== Solution ==</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; 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>\fbox{D}</math></div></td><td class='diff-marker'>+</td><td style="color: #222; 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>\fbox{D}<ins class="diffchange diffchange-inline"></math> Rotating a point <math>(x,y)</math> <math>90^{\circ}</math> anticlockwise about the origin maps it to <math>(-y,x).</math> (You can prove this geometrically, or using matrices if you aren't convinced). Thus <math>(x, \log_{10}x)</math> maps to <math>(-\log_{10}x, x)</math>, so new <math>y = </math> old <math>x = 10^{\log_{10}x} = 10^{-(-\log_{10}x)} = 10^{-\text{new} x}</math>, so the new equation is <math>y=10^{-x}.</ins></math></div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== See also ==</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== See also ==</div></td></tr>
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Hapaxoromenon
https://artofproblemsolving.com/wiki/index.php?title=1991_AHSME_Problems/Problem_24&diff=63708&oldid=prev
Timneh: /* Solution */
2014-09-28T19:56:51Z
<p><span dir="auto"><span class="autocomment">Solution</span></span></p>
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<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Revision as of 19:56, 28 September 2014</td>
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<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== Solution ==</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== Solution ==</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; 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>\fbox{}</math></div></td><td class='diff-marker'>+</td><td style="color: #222; 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>\fbox{<ins class="diffchange diffchange-inline">D</ins>}</math></div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== See also ==</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== See also ==</div></td></tr>
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Timneh
https://artofproblemsolving.com/wiki/index.php?title=1991_AHSME_Problems/Problem_24&diff=63663&oldid=prev
Timneh at 06:58, 28 September 2014
2014-09-28T06:58:46Z
<p></p>
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<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Revision as of 06:58, 28 September 2014</td>
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<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; 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 style="font-weight: bold; text-decoration: none;">== Problem ==</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; 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 style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The graph, <math>G</math> of <math>y=\log_{10}x</math> is rotated <math>90^{\circ}</math> counter-clockwise about the origin to obtain a new graph <math>G'</math>. Which of the following is an equation for <math>G'</math>?</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The graph, <math>G</math> of <math>y=\log_{10}x</math> is rotated <math>90^{\circ}</math> counter-clockwise about the origin to obtain a new graph <math>G'</math>. Which of the following is an equation for <math>G'</math>?</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>(A) <math>y=\log_{10}\left(\frac{x+90}{9}\right)</math> (B) <math>y=\log_{x}10</math> (C) <math>y=\frac{1}{x+1}</math> (D) <math>y=10^{-x}</math> (E) <math>y=10^x</math></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>(A) <math>y=\log_{10}\left(\frac{x+90}{9}\right)</math> (B) <math>y=\log_{x}10</math> (C) <math>y=\frac{1}{x+1}</math> (D) <math>y=10^{-x}</math> (E) <math>y=10^x</math></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; 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 style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; 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 style="font-weight: bold; text-decoration: none;">== Solution ==</ins></div></td></tr>
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<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; 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 style="font-weight: bold; text-decoration: none;">== See also ==</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; 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 style="font-weight: bold; text-decoration: none;">{{AHSME box|year=1991|num-b=23|num-a=25}}  </ins></div></td></tr>
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<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; 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 style="font-weight: bold; text-decoration: none;">[[Category: Intermediate Algebra Problems]]</ins></div></td></tr>
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Timneh
https://artofproblemsolving.com/wiki/index.php?title=1991_AHSME_Problems/Problem_24&diff=56421&oldid=prev
Nathan wailes at 17:54, 5 July 2013
2013-07-05T17:54:03Z
<p></p>
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<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Revision as of 17:54, 5 July 2013</td>
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<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>(A) <math>y=\log_{10}\left(\frac{x+90}{9}\right)</math> (B) <math>y=\log_{x}10</math> (C) <math>y=\frac{1}{x+1}</math> (D) <math>y=10^{-x}</math> (E) <math>y=10^x</math></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>(A) <math>y=\log_{10}\left(\frac{x+90}{9}\right)</math> (B) <math>y=\log_{x}10</math> (C) <math>y=\frac{1}{x+1}</math> (D) <math>y=10^{-x}</math> (E) <math>y=10^x</math></div></td></tr>
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Nathan wailes
https://artofproblemsolving.com/wiki/index.php?title=1991_AHSME_Problems/Problem_24&diff=51823&oldid=prev
Ckorr2003: Created page with "The graph, <math>G</math> of <math>y=\log_{10}x</math> is rotated <math>90^{\circ}</math> counter-clockwise about the origin to obtain a new graph <math>G'</math>. Which of the f..."
2013-03-17T05:33:37Z
<p>Created page with "The graph, <math>G</math> of <math>y=\log_{10}x</math> is rotated <math>90^{\circ}</math> counter-clockwise about the origin to obtain a new graph <math>G'</math>. Which of the f..."</p>
<p><b>New page</b></p><div>The graph, <math>G</math> of <math>y=\log_{10}x</math> is rotated <math>90^{\circ}</math> counter-clockwise about the origin to obtain a new graph <math>G'</math>. Which of the following is an equation for <math>G'</math>?<br />
<br />
(A) <math>y=\log_{10}\left(\frac{x+90}{9}\right)</math> (B) <math>y=\log_{x}10</math> (C) <math>y=\frac{1}{x+1}</math> (D) <math>y=10^{-x}</math> (E) <math>y=10^x</math></div>
Ckorr2003