A problem with sinh where I keep getting 3 different answers

[schlynn]

Homework Statement

This isn't a homework problem, just a thought problem. I want to find a solution to the equation sinh(x)=pi.

Homework Equations

sinh(x)=(e^x-e^-x)/2

The Attempt at a Solution

Here is a picture of the work that I did, pretty much, I set the equation for sinh equal to pi, and I found (ln(2pi)/2). Thats all one part, not the natural log of 2pi/2, that's just stupid. Any way, calculators gave my a number along the lines of 1.05 or something like that, and when I had wolframalpha solve sinh(x)=pi, they gave me a number with i and some square roots that I don't know where they came from. I just want an explanation of what's going on. When I plugged (ln(2pi)/2) into the equation for sinh, I got pi, so I showed that this give pi, but wolframalpha gives another answer, and calculators say I'm wrong. What did I do wrong? Sorry about the pictures, but I don't know LaTex.

 

[Dick]

The first thing you did wrong was saying ln(2pi+e^(-x))=ln(2pi)+ln(e^(-x)). That's completely wrong. ln(a+b) is not ln(a)+ln(b). Take your original equation and substitute u=e^x, so 1/u=e^(-x). Now it's quadratic in u. Solve for u first. Then take the log.

 

[schlynn]

Oh, I made the mistake, the property is ln(ab)=ln(a)+ln(b), fail, alright, thanks.