Log 1/2 log3 (x+1)/(x-1)≥0

[latex]\log_{1/2}\log_3\frac{x+1}{x-1}\ge0\\ 0<\log_3\frac{x+1}{x-1}\le1\\ 1<\frac{x+1}{x-1}\le3\\ \begin{cases}1<\frac{x+1}{x-1}\\\frac{x+1}{x-1}\le3\end{cases}\\ \begin{cases}\frac{2}{x-1}>0\\\frac{x-2}{x-1}\ge0\end{cases}\\ \begin{cases}x>1\\x\in(-\infty,1)\cup[2,+\infty)\end{cases}\\x\in[2,+\infty)[/latex]