Recently I encountered an exponential equation in form of $a^x + x^a = b^x$, where both $a,b$ are integers. The tricky part is $x$ appears in both the base and the exponential part.
Is this kind of equation solvable?
For instance, $6^x + x^6 = 10^x$. Where should I start from?
EDIT: There is a similar question. But this one differs from the other one in a way that it has two constants $a, b$