\[{{\log }_{3}}(x-1)\le 4-\frac{9}{{{\log }_{3}}9(x-1)}\]
\[{{\log }_{3}}(x-1)\le 4-\frac{9}{{{\log }_{3}}(x-1)+2}\]
\[t={{\log }_{3}}(x-1)\]
\[t\le 4-\frac{9}{t+2}\]
\[1={{\log }_{3}}(x-1)\]
\[\left\{ \begin{aligned}
& x=4 \\
& x<\frac{10}{9} \\
& x>1 \\
& x\ne \frac{10}{9} \\ \end{aligned} \right.\]