Question 1012270
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(log2(x) - log0.5(x) -2)/(3log2(x) +2)=4
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<pre>
Your equation is 

{{{(log(2,(x)) - log(0.5,(x)) -2)/(3*log(2,(x))+2)}}} = {{{4}}}.

First, notice that log(0.5,(x)) = -log(2,(x)). It is easy to understand if you know what the logarithm is.

Second, introduce a new variable y = log(2,(x)) for brevity.

Then your equation will take the form

{{{(y + y -2)/(3y+2)}}} = {{{4}}},   or  {{{(y-1)/(3y+2)}}} = {{{2}}}.

I am sure you can easily solve it.

The solution is y = -1.

Then you need to solve the equation 

{{{log(2,(x))}}} = -1,

which will give you the answer x = {{{1/2}}}.

<U>Answer</U>. x = {{{1/2}}}.
</pre>
Introducing new variable is the standard way to solve equations like this one.