Question

Solve the following inequality:
${\log }_{0.5}{\log }_5(x^2-4)>{\log }_{0.5}1$

Answer 1

${\log }_{0.5}{\log }_5(x^2-4)>{\log }_{0.5}1$

${\log }_5(x^2-4)<1$ & $x^2-4>0$

$x^2-4<5(x+2)(x-2)>0$

$x^2-9<0xϵ(-\infty ,-2)\bigcup (2,\infty )$

$(x+3)(x-3)<0$

$xϵ(-3,3)$

Taking intersection we get $xϵ(-3,-2)\bigcup (2,3)$