Question

Express the following in logarithmic form
$\tan h^{-1}\left(\frac{1}{2}\right)$

Answer 1

Let $tan{h}^{-1}\left(\frac{1}{2}\right)=x$

$\Rightarrow tanhx=1/2$

$\Rightarrow \frac{e^{2x}-1}{e^{2x}+1}=1/2$

$\Rightarrow e^{2x}=3$

$\Rightarrow x=\frac{1}{2}ln3$