Question

Solution set of $lo{g}_3(x^2-2)<lo{g}_3(\frac{3}{2}\left|x\right|-1)$ 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
$x^2-2>0,\frac{3}{2}\left|x\right|-1>0and{x}^2-2<\frac{3}{2}\left|x\right|-1\Rightarrow x^2>2,\left|x\right|>\frac{2}{3}and{\left|x\right|}^2-\frac{3}{2}\left|x\right|-1<0\Rightarrow \left|x\right|>\sqrt{2}and\left|x\right|<2[\because 2\left|x\right|+1>0]\Rightarrow \sqrt{2}<\left|x\right|<2\Rightarrow xϵ(-2,-\sqrt{2})\cup (\sqrt{2},2)$