Question

Solve the following inequality:
${\log }_{0.2}(x^2-x-2)>{\log }_{0.2}(-x^2+2x+3)$

Answer 1

$-{\log }_2(x^2-x-2)>-{\log }_2(-x^2+2x+3)$

${\log }_2(x^2-x-2)<{\log }_2(-x^2+2x+3)$

$x^2-x-2<-x^2+2x+3$

$2x^2-3x-5<0$

$2x^2-2x+5x-5<0$

$2x(x-1)+5(x-1)<0$

$(2x+5)(x-1)<0$

$x\epsilon (\frac{-5}{2},1)$