SOLUTION: Good evening Friends, I have some difficulties solving the following logarithmic equation: (log2(x) - log0.5(x) -2)/(3log2(x) +2)=4 Has somebody a step by step solution to help

Your equation is 

 = .

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

 = ,   or   = .

I am sure you can easily solve it.

The solution is y = -1.

Then you need to solve the equation 

 = -1,

which will give you the answer x = .

Answer. x = .