<PRE><B>Question 52057</B>
&lt;pre&gt;&lt;font size = 5&gt;&lt;b&gt;How do you evaluate 
1. log base is 12 544 ? do I divide 544 by 12?

No. 

Let the answer be x

log&lt;sub&gt;12&lt;/sub&gt;544 = x

Rewrite using rule: log&lt;sub&gt;B&lt;/sub&gt;A = C can be rewritten B&lt;sup&gt;C&lt;/sup&gt; = A 

12&lt;sup&gt;x&lt;/sup&gt; = 544

Take logs base 10 of both sides

log&lt;sub&gt;10&lt;/sub&gt;12&lt;sup&gt;x&lt;/sup&gt; = log&lt;sub&gt;10&lt;/sub&gt;544

Use rule: log&lt;sub&gt;B&lt;/sub&gt;A&lt;sup&gt;C&lt;/sup&gt; = C*log&lt;sub&gt;B&lt;/sub&gt;A

x*log&lt;sub&gt;10&lt;/sub&gt;12 = log&lt;sub&gt;10&lt;/sub&gt;544

Divide both sides by log&lt;sub&gt;10&lt;/sub&gt;12

 x*log&lt;sub&gt;10&lt;/sub&gt;12     log&lt;sub&gt;10&lt;/sub&gt;544
----------- = ----------
  log&lt;sub&gt;10&lt;/sub&gt;12      log&lt;sub&gt;10&lt;/sub&gt;12

      1
 x*&lt;s&gt;log&lt;sub&gt;10&lt;/sub&gt;12&lt;/s&gt;     log&lt;sub&gt;10&lt;/sub&gt;544
----------- = ----------
  &lt;s&gt;log&lt;sub&gt;10&lt;/sub&gt;12&lt;/s&gt;      log&lt;sub&gt;10&lt;/sub&gt;12
     1 

               log&lt;sub&gt;10&lt;/sub&gt;544
          x = ----------
               log&lt;sub&gt;10&lt;/sub&gt;12

Get your calculator and use the LOG key
to figure the right side:

          x = 2.534883653

2. log base .5 24?

It&#39;s done the same way. Answer: -4.584962501

Quicker way:

log&lt;sub&gt;B&lt;/sub&gt;C  = log&lt;sub&gt;10&lt;/sub&gt;C/log&lt;sub&gt;10&lt;/sub&gt;B

Edwin&lt;/pre&gt;</PRE>