<PRE><B>Question 61960</B>
The given expression is: 


log&lt;sub&gt;3&lt;/sub&gt;4x&lt;sup&gt;log&lt;sub&gt;3&lt;/sub&gt;4x&lt;/sup&gt; = 5


This can be written as: 


(log&lt;sub&gt;3&lt;/sub&gt;4x)(log&lt;sub&gt;3&lt;/sub&gt;4x) = 5 



==&gt; (log&lt;sub&gt;3&lt;/sub&gt;4x)^2 = 5 


Taking root on both the sides, we get: 


(log&lt;sub&gt;3&lt;/sub&gt;4x) = {{{sqrt(5)}}}


Using the definition of log, we get: 



3&lt;sup&gt;{{{sqrt(5)}}} = 4x 


(3&lt;sup&gt;{{{sqrt(5)}}}&lt;/sup&gt;/4) = x 


Hence, the solution.. 

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