Question

Solve the following inequality:
${\log }_3\frac{1-2x}{x}⩽0$

Answer 1

$\frac{1-2x}{x}>0(1-2x)x>0x\ne 0(2x-1)x<0x\in (0,\frac{1}{2})$

and

$\frac{1-2x}{x}\le 11-2x\le x\frac{1}{3}\le xx\in [\frac{1}{3},\infty )$

Taking intersection, we get

$x\in [\frac{1}{3},\frac{1}{2})$