Which of the following is not the solution of `(log)_3(x^2-2)<(log)_3(3/2|x|-1)` is `(sqrt(2),2)` (b) `(-2,-sqrt(2))` `(-sqrt(2),2` (d) none of these

Options

A. `(-sqrt2,2)`
B. `(-2, -sqrt2)`
C. ` (-sqrt2, 2)`
D. none of these

Answer

C

Explanation

We have, ` log_(3) (x^(2) - 2) lt log_(3) (3/2|x|-1)`
For this to be true, we must have
`x^(2) - 2 gt 0, 3/2 |x| - 1 gt 0`
` and x^(2) - 2 lt 3/2 |x|-1`
` rArr x ^(2) gt 2, |x|gt 2/3 and 2|x|^(2) - 3 |x|-2 lt 0`
` rArr |x| gt sqrt2, |x| gt 2/3 and (2|x|+ 1)(|x|-2) lt 0`
` rArr |x| gt sqrt2 and |x| lt 2`
` rArr sqrt2 lt |x| lt 2`
` rArr x in (-2, - sqrt2) cup(sqrt2, 2)`