Solve ` log_(2).(x-1)/(x-2) gt 0 ` .

Explanation

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

### Step 1: Rewrite the Inequality
The inequality \( \log_{2}\left(\frac{x-1}{x-2}\right) > 0 \) implies that the argument of the logarithm must be greater than 1 because the logarithm of a number is positive if that number is greater than 1.

### Step 2: Set Up the Inequality
We set up the inequality:
\[
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