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  4. Let S= log 2(√7+√5), then the value of log 2(√7-√5) in terms of S, is

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Q. Let $S=\log _2(\sqrt{7}+\sqrt{5})$, then the value of $\log _2(\sqrt{7}-\sqrt{5})$ in terms of $S$, is

Continuity and Differentiability

Solution:

$\log _2(\sqrt{7}-\sqrt{5})=\log _2\left(\frac{2}{\sqrt{7}+\sqrt{5}}\right)=\log _2 2-\log _2(\sqrt{7}+\sqrt{5})=1- S$