Проверьте логарифмическое неравенство

Решите задачу:

$log_{(x-1)^2}\, (x^2-4x+4)\ \textless \ 0\\\\log_{(x-1)^2}\, (x-2)^2\ \textless \ 0\\\\ODZ:\; \; \left\{\begin{array}{c}(x-2)^2\ \textgreater \ 0\\(x-1)^2\ \textgreater \ 0\\(x-1)^2\ne 1\end{array}\right \; \left\{\begin{array}{c}x\ne 2\\x\ne 1\\x\ne 0\; ,\; x\ne 2\end{array}\right \; \to \; \; x\ne 0,\; x\ne 1,\; x\ne 2\\\\((x-1)^2-1)(x^2-4x+4-1)\ \textless \ 0\\\\(x^2-2x)(x^2-4x+3)\ \textless \ 0\\\\x(x-2)(x-1)(x-3)\ \textless \ 0\\\\+++(0)---(1)+++(2)---(3)+++\\\\x\in (0,1)\cup (2,3)$