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View Full Version : Natural Logs and inverse functions


b200w
Jan21-09, 05:21 PM
1. The problem statement, all variables and given/known data
Find the inverse equation (i.e. solve for x)
y=(e^x)/(1+2e^x)


2. The attempt at a solution
e^x = y(1+2e^x)
x = ln(y) + ln(1+2e^x)
???
Profit!

I can't figure out what to do with ln(1+2e^x) to get the x out of there so I can finish isolating x. I tried balancing it another way and ended up with x = ln(e^x - y) - ln(2y) which as far as I can tell is worse. Any suggestions? As far as I can tell I'm probably just missing something obvious but I've been sitting here for a while trying to figure it out...

Mark44
Jan21-09, 05:29 PM
Starting with y = e^x/(1 + 2e^x),
multiply both sides by (1 + 2e^x).

Get all the terms that involve e^x on one side, and all other terms on the other side.
Factor e^x out of the terms that have this factor and divide both sides by the factor that isn't e^x.

b200w
Jan21-09, 05:38 PM
*facepalm* Thank you... I don't know why I couldn't figure that out...