Question

log 1/2 log3 (x+1)/(x-1)≥0

Answer 1

$log_{1/2}log_3frac{x+1}{x-1}ge0\ 0<log_3frac{x+1}{x-1}le1\ 1<frac{x+1}{x-1}le3\ begin{cases}1<frac{x+1}{x-1}\frac{x+1}{x-1}le3end{cases}\ begin{cases}frac{2}{x-1}>0\frac{x-2}{x-1}ge0end{cases}\ begin{cases}x>1\xin(-infty,1)cup[2,+infty)end{cases}\xin[2,+infty)$