# Logarithms

Algebra Level 3

Let $$f(x) = \log_2 x$$ be a function whose domain is $$x>0$$. If $$a> b$$ are positive numbers satisfying $$\dfrac{a+b}{a-b} = 64$$, find

$\dfrac12 f( a^2+b^2 + 2ab) - f\left( \sqrt{a^2-b^2} \right) .$

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