Question

If $\cos h^{-1}x=2{\log }_e(\sqrt{2}+1)$, then $x=$

• A. $1$
• B. $2$
• C. $4$
• D. $3$

Answer 1

Answer: (D)

$3$

Given, $\cos h^{-1}x=2{\log }_e(\sqrt{2}+1)$

Therefore, ${\cosh }^{-1}x={\log }_e{(\sqrt{2}+1)}^2$

$\log (x+\sqrt{x^2-1})={\log }_e(3+2\sqrt{2})$

$\log (x+\sqrt{x^2-1})=\log (3+\sqrt{9-1})$

by comparing we get $x=3$