I have a truly simple inequality, which I want to prove using Mathematica:
$$ a^x \geq 1 ,\quad \quad with \quad 1\leq a \quad and \quad 1\leq x \quad a,x \in R$$
This is obviously true. When I try to solve this in Mathematica using for example:
Assuming[1 <= a && x >= 1, FullSimplify[a^x >= 1]]
the only output I get, is
a^x >= 1 and not the desired
True. Is Mathematica really not able to solve this simple problem or am I missing something basic here?
Of course, my real inequality is much more complicated, but I broke it down until I identified working with exponents as the problem here.