Using Natural Logarithms to solve for x

[adillhoff]

Homework Statement

Use Natural Logarithms to solve for x in terms of y

$$y = \frac{e^{10x}+e^{-10x}}{e^{10x}-e^{-10x}}$$

Homework Equations

I am not too sure.

The Attempt at a Solution

I multiplied both sides by the denominator first.
Then I multiply by an LCD of $$e^{10x}$$
I end up with $$y(e^{20x})-y = (e^{20x})+1$$

EDIT: I don't really know where to go from here. Any direction would be greatly appreciated.

 

[micromass]

From were you ended up, you could proceed by putting all terms of the form $$e^{20x}$$ to one side of the equation. Then factor it out and take the logarithm.

 

[adillhoff]

From were you ended up, you could proceed by putting all terms of the form $$e^{20x}$$ to one side of the equation. Then factor it out and take the logarithm.

Absolutely. Thank you so much for the help. I ended up with

$$x=\frac{ln\frac{y+1}{y-1}}{20}$$