Решить неравенство: [latex] log(_{x-1})^{2}\ x^{2} \leq 1[/latex]  

[latex]\log_{(x-1)^2}x^2 \leq 1\\ \log_{(x-1)^2}\frac{x^2}{(x-1)^2}\leq0\\ \begin{cases} ((x-1)^2-1)\left(\frac{x^2}{(x-1)^2}-1\right)\le0\\ x\not\in\lbrace0,1,2\rbrace \end{cases}\\ \begin{cases} x(x-2)(2x-1)\le0\\ x\not\in\lbrace0,1,2\rbrace \end{cases}\\ x\in(-\infty,0)\cup[0.5,1)\cup(1,2)[/latex]