# Ajitesh's function

Algebra Level 4

Consider a function $$f$$ from the real numbers to the real numbers, such that $$2f(xy) = [{f(x)}]^y + [{f(y)}]^x$$ for all real values $$x,y$$, and $$f(1) =2$$. If $$\sum_{i=1}^{100} f(i)$$ can be written as $$2^a-2$$, what is $$a$$?

This problem is posed by Ajitesh M.

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