When I write graph for fun I found that there is some value a that make $y=a^x$ and $y=\log_a (x)$ don't touch each other and there is some value a that make $y=a^x$ and $y=\log_a (x)$ intersect each other too (2 intersect point). Because of this there is a value a that make they touch each other.
So, I try to find that value by writing graph. Then, I get a = 1.4444... or 13/9. But I have no idea why a = 13/9.
Please help me or guide how to prove that.