sinh^{-1}left(2^{3/2}right) is equal to : | vedclass

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Question

(A) We know that the formula for the inverse hyperbolic sine function is $\sinh^{-1}(x) = \log\{x + \sqrt{x^2 + 1}\}$.Substituting $x = 2^{3/2}$ into

Vedclass · Accepted Answer

$\log(3+\sqrt{8})$

Vedclass · Answer

(A) We know that the formula for the inverse hyperbolic sine function is $\sinh^{-1}(x) = \log\{x + \sqrt{x^2 + 1}\}$.Substituting $x = 2^{3/2}$ into the formula:$\sinh^{-1}(2^{3/2}) = \log\{2^{3/2} + \sqrt{(2^{3/2})^2 + 1\}}$.Since $2^{3/2} = \sqrt{2^3} = \sqrt{8}$,we have:$\sinh^{-1}(2^{3/2}) = \log\{\sqrt{8} + \sqrt{8 + 1\}}$.$= \log\{\sqrt{8} + \sqrt{9\}}$.$= \log\{3 + \sqrt{8\}}$.Thus,the correct option is $A$.

$\sinh^{-1}\left(2^{3/2}\right)$ is equal to :

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