Question

The number of solutions of $3^{|x|}(|2-|x||)=1$ is

• A. $2$
• B. $6$
• C. $4$
• D. $8$

Answer 1

The correct option is C $4$

$3^{|x|}(|2-|x||)=1\Rightarrow |2-|x||=3^{-|x|}$

We know graph of $|x|$


Graph of $-|x|$


For $2-|x|$ move $-|x|$ by $2$ units upwards.


Now graph of $|2-|x||$


Graph of $3^{-|x|}$


For no. of solutions


Hence, the number of solutions is $4$.