Q. $\sinh^{- 1}{(2^{3/2})}$ is equal to
A) $\log{(3 + \sqrt{8})}$
B) $\log{(3 - \sqrt{8})}$
C) $\log{(2 + \sqrt{18})}$
D) $\log{(\sqrt{8} + \sqrt{27})}$
Explanation
(a)
${\sinh^{- 1}(2)}^{3/2} = \log{(2^{3/2} + \sqrt{\left( 2^{\frac{3}{2}} \right)^{2} + 1})}$
$= \log{(\sqrt{8} + \sqrt{8 + 1})}$
$= \log{(3 + \sqrt{8})}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.