# 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

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

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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