Answer
The line $x=2^y$ is the inverse of the line $y=2^x$.
Work Step by Step
The blue line is $y=2^x$, and the black line is $x=2^y$.
Two points on the blue line are $(0,1)$ and $(2,4)$. Two points on the black line are $(1,0)$ and $(4,2)$.
Since the coordinates of points on the black line are the reversed coordinates of points on the blue line, then the black line is the inverse function of the