Number of solutions of 2 ^ ( | x | ) = 3 ^ | x | in [ - π, π ] , is...

In the interval $\left[– \pi, \pi\right]$ all the values of $sin | x |$ are positive as well as $| \cos x |$
Hence in \left[– \pi, \pi\right]$, equation gets reduced to, </p><p>${2}^{sin x} = {3}^{cos x}$<br />Taking log on both sides,<br />$sin xlog 2 = cos xlog 3$<br />$⇒ \left|\tan x\right| = \log 3 / \log 2$, value of$\tan x$are positive in${1}^{st} and {3}^{rd}$quadrant and negative in${2}^{nd} and {4}^{th}$quadrant but positive for \left|\tan x\right|$ in all the values of $x in \left[– \pi, \pi\right].</p><p>Hence,$\tan x$will repeat its value in all$4$quadrants, so the number of solutions are$4$.</p>$