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
We need to analyze the expression \(\frac{\log_2(x-1)}{x-2}\) and determine when it is greater than 0. This will occur when both the numerator and denominator are either both positive or both negative.

### Step 2: Determine the domain
The logarithm \(\log_2(x-1)\) is defined only when \(x-1 > 0\), which means \(x > 1\). Also, the denominator \(x-2\) cannot be zero, so \(x \neq 2\).

...