Originally Posted by
HallsofIvy Because they are "inverse" functions just as your title implies.
If $\displaystyle y= 2^x$, then taking logarithm, base 2, of both sides, $\displaystyle log_2(y)= x$. Since the graph of a function is typically of y= f(x), your graph is of $\displaystyle y= log_2(x)$. The two graphs, of $\displaystyle y= 2^x$, which is the same as the graph of $\displaystyle x= log_2(y)$, and $\displaystyle y= log_2(x)$ just have x and y reversed: (0, 1) on one graph becomes (1, 0) on the other.
This is a general property of graphs of "inverse" functions: The point (a, b) on one corresponds to (b, a) on the other.