Question

Solve the following equation giving your answers in terms of natural logarithms
$3\sin hx-\cos hx=1$

Answer 1

$3\sin hx-\cos hx=1$

$3\left(\frac{e^x-e-x}{2}\right)-\frac{e^x+e^{-x}}{2}=1$

$e^{2x}-2e^x-2=0$

$e^x=-1$ or $2$

So, $x=-1$ should be neglected.

$x=log\left(2\right)$