Question

Solve the following inequality:
${\log }_{4}x-13{\log }^{2}x+36>0$

Answer 1

${\log }^{4}x-13{\log }^{2}x+36>0$

$({\log }^2-4)({\log }^{2}x-9)>0$

$(\log x+2)(\log x-2)(\log x+3)(\log x-3)>0$

$\log xϵ(-\infty ,-3)\bigcup (-2,2)\bigcup (3,\infty )$

$xϵ(0,\frac{1}{{10}^2})\bigcup (\frac{1}{100},100)\bigcup (1000,\infty )$