Similar to how $log(xy) = log(x) + log(y)$, does a nontrivial function exist that has the property $f(x^y) = f(x)f(y)$? How would one attempt to derive such a function?
2026-04-12 16:57:57.1776013077
Does a function that has an exponential analog to $log(xy) = log(x) + log(y)$ exist?
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Then $f(x^y) = f(y^x) \Rightarrow f(1^y) = f(y^1) \Rightarrow f(1) = f(y)$ for any $y$. f is a constant function, $0$ or $1$.