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  4. If b=√3+2 √2+√3-2 √2, then the value of log b 64 is equal to

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Q. If $b=\sqrt{3+2 \sqrt{2}}+\sqrt{3-2 \sqrt{2}}$, then the value of $\log _b 64$ is equal to

Continuity and Differentiability

Solution:

Given, $b =\sqrt{3+2 \sqrt{2}}+\sqrt{3-2 \sqrt{2}}=(\sqrt{2}+1)+(\sqrt{2}-1)=2 \sqrt{2}$
$\therefore \log _b 64=\log _{2^{3 / 2}} 2^6=\frac{6}{3 / 2}==4$.