Question

Solve the following inequality:
${\log }_{0.5}(x^2-5x+6)>-1$

Answer 1

$x^2-5x+6>0(x-3)(x-2)>0x\in (-\infty ,2)\cup (3,\infty )$

and

$\frac{\log (x^2-5x+6)}{-\log 2}>-1\log (x^2-5x+6)<\log 2x^2-5x+6<2x^2-5x+4<0(x-4)(x-1)<0x\in (1,4)$

Taking intersection, we get

$x\in (1,2)\cup (3,4)$