<PRE><B>Question 67161</B>
&lt;pre&gt;&lt;font size = 5&gt;&lt;b&gt;log&lt;sub&gt;4&lt;/sub&gt;(4x) + 2·log&lt;sub&gt;4&lt;/sub&gt;(x + 3) = 2

Get the left side to a single logarithm.

Use the rule

 n·log&lt;sub&gt;B&lt;/sub&gt;A = log&lt;sub&gt;B&lt;/sub&gt;A&lt;sup&gt;n&lt;/sup&gt;  

to rewrite the second term:

log&lt;sub&gt;4&lt;/sub&gt;(4x) + log&lt;sub&gt;4&lt;/sub&gt;(x + 3)&lt;sup&gt;2&lt;/sup&gt; = 2

Use the rule:

 log&lt;sub&gt;B&lt;/sub&gt;A + log&lt;sub&gt;B&lt;/sub&gt;C = log&lt;sub&gt;B&lt;/sub&gt;(AC) to rewrite the
whole left side:

        log&lt;sub&gt;4&lt;/sub&gt;[4x(x + 3)&lt;sup&gt;2&lt;/sup&gt;] = 2

Use the rule:

log&lt;sub&gt;B&lt;/sub&gt;A = C can be rewritten as A = B&lt;sup&gt;C&lt;/sup&gt; 

to rewrite the equation:

          4x(x + 3)&lt;sup&gt;2&lt;/sup&gt; = 4&lt;sup&gt;2&lt;/sup&gt;

    4x(x + 3)(x + 3) = 16

4x(x&lt;sup&gt;2&lt;/sup&gt; + 3x + 3x + 9) = 16

     4x(x&lt;sup&gt;2&lt;/sup&gt; + 6x + 9) = 16

To make things easier, divide both sides by 4

      x(x&lt;sup&gt;2&lt;/sup&gt; + 6x + 9) = 4     

       x&lt;sup&gt;3&lt;/sup&gt; + 6x&lt;sup&gt;2&lt;/sup&gt; + 9x = 4

   x&lt;sup&gt;3&lt;/sup&gt; + 4x&lt;sup&gt;2&lt;/sup&gt; + 9x - 4 = 0 

There is no easy way to solve that by hand, so we
use a TI-82 or higher calculator and get

            x = 0.3553013976 
Edwin&lt;/pre&gt; </PRE>