# Logs can be difficult

Calculus Level 4

Given that $$\displaystyle f(x) = \int_1^x \log_{1/2} \left(1-2^{-t} \right) \, dt$$ and $$f(2) + f(2- \log_2 3) = a - b \log_b c$$, where $$a,b$$ and $$c$$ are prime numbers. Find $$a+b+c$$.

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