Question

Solve:
$5^{{\log }_{\sqrt{5}}x}-x-6<0$

Answer 1

$5^{{\log }_{\sqrt{5}}x}-x-6<0$

$5^{2{\log }_{5}x}-x-6<0$

$5^{{\log }_5{x}^3}-x-6<0$

$x^2-x-6<0$

$x^2-3x+2x-6<0$

$x(x-3)+2(x-3)<0$

$x-3(x+2)<0$

$\Rightarrow x,\in (-2,3)$