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Natural Logs and inverse functions

  1. Jan 21, 2009 #1
    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...
     
    Last edited: Jan 21, 2009
  2. jcsd
  3. Jan 21, 2009 #2

    Mark44

    Staff: Mentor

    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.
     
  4. Jan 21, 2009 #3
    *facepalm* Thank you... I don't know why I couldn't figure that out...
     
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