Question

If sinh x = 3 then show that x = $log_e (3 + \sqrt{10})$.

Answer 1

Given that

sinh x = 3

so we have

$x = sin h^{-1} 3$

We know that

$sin h^{-1}y=log_{e}(y+\sqrt{y^{2}+1})$

Putting y = 3 , we get

$x=sin h^{-1}(3)\\\\x=log_{e}(y+\sqrt{y^{2}+1}) \\\\x=log_{e}(3+\sqrt{3^{2}+1})\\\\x=log_{e}(3+\sqrt{10})$

Which is the required Answer