# A somewhat simple equation

• October 6th 2005, 02:23 PM
a4swe
A somewhat simple equation
I just got stuck and is without tutoring for the weekend, I found this forum after some searching on the net and hope to find help here.

Can anyone solve:
$e^x-e^{-x}=6$ or if you wish sineh(x)=3?

Edit: Maybe I should add, it's not an answer I am looking for more like a solution or maybe a hint.
• October 6th 2005, 04:19 PM
hpe
Quote:

Originally Posted by a4swe
Can anyone solve:
$e^x-e^{-x}=6$ or if you wish sineh(x)=3?

Set $z = e^x$ and thus $e^{-x} = \frac{1}{z}$. Then your equation becomes
$z - \frac{1}{z} = 6$ or $z^2 - 1 = 6z$.
This is a quadratic equation that you can solve with the usual methods. Then solve for $x$. Works for all equations of the form $\cosh x = a$ or $\sinh x = a$.
• October 7th 2005, 12:47 AM
a4swe
Thank you for a perfect answer.