Question

Express the following function in logarithmic form:
$\sin h^{-1}\left(\frac{3}{4}\right)$

Answer 1

Let $sin{h}^{-1}\left(\frac{3}{4}\right)=x$

$\Rightarrow sinhx=3/4$

$\Rightarrow \frac{e^x-e^{-x}}{2}=3/4$

$\Rightarrow (2e^{2x}+1)(e^x-2)=0$

$\Rightarrow e^x=2$ {Since $e^{2x}=\frac{-1}{2}$ is not possible}

$\Rightarrow x=sin{h}^{-1}\left(\frac{3}{4}\right)=ln2$