Question

Solve the following inequality:
${\log }_{1.5}\frac{2x-8}{x-2}<0$

Answer 1

$\frac{2x-8}{x-2}>0(2x-8)(x-2)>0x\ne 2x\in (-\infty ,2)\cup (4,\infty )$

and

$\frac{2x-8}{x-2}<12x-8<x-2x<6x\in (-\infty ,6)$

Taking intersection, we get

$x\in (-\infty ,2)\cup (4,6)$