Solve : `(log)_2(x-1)/(x-2)>0`

Explanation

To solve the inequality \(\frac{\log_2(x-1)}{x-2} > 0\), we will follow these steps:

### Step 1: Understand the Inequality
The inequality \(\frac{\log_2(x-1)}{x-2} > 0\) means that the fraction is positive. A fraction is positive if both the numerator and denominator are either both positive or both negative.

### Step 2: Determine the Conditions for the Numerator
The numerator \(\log_2(x-1)\) is positive when \(x-1 > 1\), which simplifies to:
\[
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