Question

The value of ${\sinh }^{-1}\left(3\right)$

• A. $\log (1+\sqrt{2})$
• B. $\log (2+\sqrt{3})$
• C. $\log (3+\sqrt{5})$
• D. $\log (3+\sqrt{10})$

Answer 1

The correct option is D $\log (3+\sqrt{10})$

${\sinh }^{-1}\left(3\right)$
$=\log (x+\sqrt{x^2+1}{)}_{x=3}$
$=\log (3+\sqrt{10})$.
Hence
${\sinh }^{-1}\left(3\right)=\log (3+\sqrt{10})$.