For real

Algebra Level 2

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

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

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