Question

Number of roots of $7^{\left|x\right|}\left(\left|5-\left|x\right|\right|\right)=1$ are .....

Answer 1

$7^{|x|}(|5-|x||)=1$

$⟹|5-|x||=7^{-|x|}$

From the graph

No of points of intersection of $y=7^{-|x|}$ and $y=|5-|x||$ is $4$

So the number of solutions is $4$