For real

Algebra Level 2

Suppose ff is a continuous, positive real-valued function such that f(x+y)=f(x)f(y)f(x + y) = f(x)f(y) for all real x,y.x,y.

If f(8)=3f(8) = 3 then log9(f(2015))=ab\log_{9}(f(2015)) = \dfrac{a}{b}, where aa and bb are positive coprime integers. Find ab.a - b.

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