log (9+3 sqrt{2}(2+sqrt{5})+4 sqrt{5})= | vedclass

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(B) We have,$\log (9+3 \sqrt{2}(2+\sqrt{5})+4 \sqrt{5})$$= \log (9+6 \sqrt{2}+3 \sqrt{10}+4 \sqrt{5})$$= \log ((3+\sqrt{10})(3+2 \sqrt{2}))$$= \log (3

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$\cosh ^{-1} 3+\sinh ^{-1} 3$

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(B) We have,$\log (9+3 \sqrt{2}(2+\sqrt{5})+4 \sqrt{5})$$= \log (9+6 \sqrt{2}+3 \sqrt{10}+4 \sqrt{5})$$= \log ((3+\sqrt{10})(3+2 \sqrt{2}))$$= \log (3+\sqrt{10}) + \log (3+\sqrt{8})$$= \log (3+\sqrt{3^2+1}) + \log (3+\sqrt{3^2-1})$Using the identities $\sinh^{-1}(x) = \log(x + \sqrt{x^2+1})$ and $\cosh^{-1}(x) = \log(x + \sqrt{x^2-1})$ for $x \ge 1$,we get:$= \sinh^{-1} 3 + \cosh^{-1} 3$

$\log (9+3 \sqrt{2}(2+\sqrt{5})+4 \sqrt{5})=$

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