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	<id>https://wiki.math.ucr.edu/index.php?action=history&amp;feed=atom&amp;title=004_Sample_Final_A%2C_Problem_19</id>
	<title>004 Sample Final A, Problem 19 - Revision history</title>
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	<updated>2026-04-29T10:56:39Z</updated>
	<subtitle>Revision history for this page on the wiki</subtitle>
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	<entry>
		<id>https://wiki.math.ucr.edu/index.php?title=004_Sample_Final_A,_Problem_19&amp;diff=825&amp;oldid=prev</id>
		<title>MathAdmin: Created page with &quot;&lt;span class=&quot;exam&quot;&gt; Solve for ''x'': &amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;math&gt;\log_6 \frac{1}{36} = x&lt;/math&gt; {| class=&quot;mw-collapsible mw-collapsed&quot; style = &quot;text-align:left;&quot; !Foundatio...&quot;</title>
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		<updated>2015-06-01T05:51:14Z</updated>

		<summary type="html">&lt;p&gt;Created page with &amp;quot;&amp;lt;span class=&amp;quot;exam&amp;quot;&amp;gt; Solve for &amp;#039;&amp;#039;x&amp;#039;&amp;#039;:      &amp;lt;math&amp;gt;\log_6 \frac{1}{36} = x&amp;lt;/math&amp;gt; {| class=&amp;quot;mw-collapsible mw-collapsed&amp;quot; style = &amp;quot;text-align:left;&amp;quot; !Foundatio...&amp;quot;&lt;/p&gt;
&lt;p&gt;&lt;b&gt;New page&lt;/b&gt;&lt;/p&gt;&lt;div&gt;&amp;lt;span class=&amp;quot;exam&amp;quot;&amp;gt; Solve for ''x'': &amp;amp;nbsp;&amp;amp;nbsp;&amp;amp;nbsp;&amp;amp;nbsp; &amp;lt;math&amp;gt;\log_6 \frac{1}{36} = x&amp;lt;/math&amp;gt;&lt;br /&gt;
{| class=&amp;quot;mw-collapsible mw-collapsed&amp;quot; style = &amp;quot;text-align:left;&amp;quot;&lt;br /&gt;
!Foundations&lt;br /&gt;
|-&lt;br /&gt;
|How do we remove logs from an equation?&lt;br /&gt;
|-&lt;br /&gt;
|Answer:&lt;br /&gt;
|-&lt;br /&gt;
|The definition of the logarithm tells us that if &amp;lt;math&amp;gt;\log_6(x)=y&amp;lt;/math&amp;gt;, then &amp;lt;math&amp;gt;6^y=x&amp;lt;/math&amp;gt;.&lt;br /&gt;
|-&lt;br /&gt;
|&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
Solution:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;mw-collapsible mw-collapsed&amp;quot; style = &amp;quot;text-align:left;&amp;quot;&lt;br /&gt;
! Step 1:&lt;br /&gt;
|-&lt;br /&gt;
|By the definition of the logarithm, &amp;lt;math&amp;gt;\log_6 \frac{1}{36} = x&amp;lt;/math&amp;gt; means &amp;lt;math&amp;gt;6^x=\frac{1}{36}&amp;lt;/math&amp;gt;.&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;mw-collapsible mw-collapsed&amp;quot; style = &amp;quot;text-align:left;&amp;quot;&lt;br /&gt;
! Step 2:&lt;br /&gt;
|-&lt;br /&gt;
|Now, we can solve for &amp;lt;math&amp;gt;x&amp;lt;/math&amp;gt;. Since &amp;lt;math&amp;gt;6^x=\frac{1}{36}&amp;lt;/math&amp;gt;,&lt;br /&gt;
|-&lt;br /&gt;
|we must have &amp;lt;math&amp;gt;x=-2&amp;lt;/math&amp;gt;.&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;mw-collapsible mw-collapsed&amp;quot; style = &amp;quot;text-align:left;&amp;quot;&lt;br /&gt;
! Final Answer:&lt;br /&gt;
|-&lt;br /&gt;
| &amp;lt;math&amp;gt;x=-2&amp;lt;/math&amp;gt;&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
[[004 Sample Final A|&amp;lt;u&amp;gt;'''Return to Sample Exam&amp;lt;/u&amp;gt;''']]&lt;/div&gt;</summary>
		<author><name>MathAdmin</name></author>
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