Answer:
Option D
Explanation:
We have, $\cosh^{-1} x=2 \log_{e} (\sqrt{2}+1),$
$\Rightarrow$ $\log_{e}(x+\sqrt{x^{2}-1})= \log_{e}(\sqrt{2}+1)^{2}$
$\Rightarrow$ $x+\sqrt{x^{2}-1}= (\sqrt{2}+1)^{2}$
$\Rightarrow$ $x+\sqrt{x^{2}-1}= 3+2\sqrt{2}=3+\sqrt{8}$
On comparing rational and irrational part, we get
x=3
