Question

Solve the following inequality:
${\log }_{1/3}\left({\log }_4\right(x^2-5\left)\right)>0$

Answer 1

$-{\log }_3\left({\log }_4(x^2-5)\right)>0$

${\log }_3\left({\log }_4(x^2-5)\right)<0$

$0<{\log }_4(x^2-5)<1$

$1<x^2-5<4$

$6<x^2<9Now,x^2>6and{x}^2<9$

$x^2-6>0and{x}^2-9<0$

$(x-\sqrt{6})(x+\sqrt{6})>0and(x-3)(x+3)<0$

$x\epsilon (-\infty ,-\sqrt{6})\cup (\sqrt{6},\infty )andx\epsilon (-3,3)$

$thus,$

$x\epsilon (-3,-\sqrt{6})\cup (\sqrt{6},3)$