${{\log }_{3}}{{\left( x-1 \right)}^{2}}-\frac{2}{3}{{\log }_{3}}{{x}^{3}}>0\left( 1 \right)$ điều kiện $\left\{ \begin{align}  & x\ne 1 \\  & x>0 \\ \end{align} \right.$

$\left( 1 \right)\Leftrightarrow \frac{\left| x-1 \right|}{x}>1\Leftrightarrow \left| x-1 \right|>x\Leftrightarrow \left[ \begin{align}  & x-1>x\forall x>1 \\  & 1>2x\forall x\in \left( 0;1 \right) \\ \end{align} \right.\Leftrightarrow 0