Hi Plato, Sorry for my bad English .
here I drew them.
as you can see the graph, black line is the graph of log, my question is why does it inverse? and the red one is the graph of Y=2^x.
we know that any base with exponent zero gives 1 right? but why the '1' on black one(log one) is on X axis and on the other one is on Y axis?
Because they are "inverse" functions just as your title implies.
If , then taking logarithm, base 2, of both sides, . Since the graph of a function is typically of y= f(x), your graph is of . The two graphs, of , which is the same as the graph of , and 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.