I would like to know if there is a name given to equations like the following:
or more generally:
The formatting doesn't really matter, I'm just talking about an equation where there are variables both in an exponent and in another term in a base. Another example would be this:
$$20x^2 = e^x$$
I've searched for things like "composite exponential functions" but to no avail.
Also, I guess I could solve my example by rearranging so that there is an expression containing x on the left and an exponential one on the right. Then I could graph each side and see where they equal. However, is there a way to do it analytically?
Perhaps I'm not explaining this as clearly as I could be, but I would appreciate any advice you could offer.