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Question

Question: \[\log(3 + 2\sqrt{2}) =\]...

log⁡(3+22)=\log(3 + 2\sqrt{2}) =

A

sinh⁡−13\sinh^{- 1}3

B

cosh⁡−13\cosh^{- 1}3

C

tanh⁡−13\tanh^{- 1}3

D

cos⁡h−13{\cos h}^{- 1}3

Answer

cosh⁡−13\cosh^{- 1}3

Explanation

Solution

log⁡(3+22)=log⁡(3+8)\log(3 + 2\sqrt{2}) = \log(3 + \sqrt{8}) = log⁡(3+9−1)=log⁡(3+32−1)\log ( 3 + \sqrt { 9 - 1 } ) = \log \left( 3 + \sqrt { 3 ^ { 2 } - 1 } \right) log⁡(3+22)=cos⁡h−13\log(3 + 2\sqrt{2}) = {\cos h}^{- 1}3