Question

Solution set of ${\log }_3(x^2-2)<{\log }_3(\frac{3}{2}|x|-1)$ is

• A. $(-\sqrt{2},-1)$
• B. $(-2,-\sqrt{2})$
• C. $(-\sqrt{2},2)$
• D. None of these

Answer 1

The correct option is D None of these

We must have $x^2-2>0,\frac{3}{2}|x|-1>0$,
and $x^2-2<\frac{3}{2}|x|-1$

$\Rightarrow x^2>2,|x|>\frac{2}{3}$
and $|x{|}^2-\frac{3}{2}|x|-1<0$

$\Rightarrow |x|>\sqrt{2}$ and $|x|<2$
$[\therefore 2|x|+1>0]$

$\Rightarrow \sqrt{2}<|x|<2$
$\Rightarrow x\in (-2,-\sqrt{2})\cup (\sqrt{2},2)$