# Exponential functional equations?

Algebra Level 4

$\large f(2^x)=2^{f(x)}$

Let $$f$$ satisfy the equation above with $$f(0) = 1$$. If $$f(2048)$$ can be expressed as $$a^b$$, where $$a$$ and $$b$$ are positive integers with $$a$$ prime, find $$a+b$$.

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