Question

Solve the following inequality:
${\log }_{1/3}\frac{2-3x}{x}⩾-1$

Answer 1

$\frac{2-3x}{x}>0(2-3x)x>0x\ne 0(3x-2)x<0x\in (0,\frac{2}{3})$

and

$\frac{-\log \left(\frac{2-3x}{x}\right)}{\log 3}\ge -1\frac{2-3x}{x}\le 32-3x\le 3x2\le 6x\frac{1}{3}\le x$

Taking intersection, we get

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