Solve the following equation:

$$
\log _{3}(3-x)=\sqrt{\sqrt{x-1}-\frac{1}{\sqrt{x-1}}}
$$
The domain of interpretation of the equation is $2 \leq x<3$, but if $2<x<3$, then the left side is negative. Therefore, from the coincidence of the domain of interpretation and the set of values, $x=2$ is the solution.