Question

Solve the following inequality:
$|{\log }_{3}x|-{\log }_{3}x-3<0$

Answer 1

$0<x<1-{\log }_{3}x-{\log }_{3}x-3<0{\log }_{3}x+{\log }_{3}x+3>02{\log }_{3}x>3x^2>3^{-3}{x}^2-\frac{1}{27}>0x\in (-\infty ,\frac{-1}{3\sqrt{3}})\cup (\frac{1}{3\sqrt{3}},\infty )$

Taking intersection,

$x\in (0,\frac{1}{3\sqrt{3}})$