Is nᵐ>mⁿ if m>n? I remember playing with my calculator when I was young. I really liked big numbers so I'd punch big numbers like $20^{30}$ to see how big it really is.
On such a quest, I did observe that $20^{30}$ is greater than the value of $30^{20}$. In fact, in many cases, I found that $n^m>m^n$ if $m>n$.
Is this a general fact? If so, can it be proved?

This is not an answer  I just need to show the graph. I forgot to label axis. Horizontal is $n$ and the other is $m$
Hope you like it

