# How do you solve for x in y=(e^x-e^-x)/6 ?

Dec 21, 2016

$x = {\sinh}^{-} 1 \left(3 y\right)$

#### Explanation:

$3 y = \frac{{e}^{x} - {e}^{-} x}{2}$

It has been found that $\sinh x = \frac{{e}^{x} - {e}^{-} x}{2}$, where $y = \sinh x$ is the hyperbolic sine function.

Thus,

$3 y = \sinh x$

${\sinh}^{-} 1 \left(3 y\right) = x$

I'm not entirely sure that this is the answer you want. If you want something else, write a note and I'll change the answer accordingly.

Hopefully this helps!