Question

If $3{\log }_3|-x|={\log }_3{x}^2,$ then the possible value(s) of $x$ is/are

• A. $-1$
• B. $0$
• C. $1$
• D. $2$

Answer 1

Answer: (A), (C)

The correct options are
A $-1$
C $1$

We have,
$3{\log }_3|-x|={\log }_3{x}^2$
$|-x|>0\&x^2>0\Rightarrow x\in R-\left\{0\right\}....\left(1\right)$

$\Rightarrow {\log }_3|-x{|}^3={\log }_3{x}^2$
$\Rightarrow |-x{|}^3=x^2$
$\Rightarrow |x{|}^3=x^2\Rightarrow |x{|}^2(|x|-1)=0\Rightarrow x=0,x=\pm \mathrm{1....}\left(2\right)$

From $\left(1\right)$ and $\left(2\right)$
$x=\pm 1$