Question

The number of real solutions of the equation $3^{-|x|}-2^{|x|}=0$ is

• A. $0$
• B. $1$
• C. $2$
• D. $3$

Answer 1

The correct option is B $1$

The graph of the above function cuts the x axis at 0 only.
Hence there is only one real solution.
$3^{-|x|}-2^{|x|}=0$
$3^{-|x|}=2^{|x|}$
$1=6^{|x|}$
Taking log we get
$\log \left(1\right)=|x|\log \left(6\right)$
$|x|\log \left(6\right)=0$
Since $\log \left(6\right)$ is a constant, $|x|=0$