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Inverse of a logarithmic function

  1. Jan 5, 2012 #1
    1. The problem statement, all variables and given/known data
    Greetings everyone! I am having problems getting started with this question, which asks:

    Find the inverse of [itex]y = \frac{3-4e^x}{6-10e^x}[/itex]

    2. Relevant equations



    3. The attempt at a solution

    I'm usually pretty good with these kinds of problems, but for some reason I seem to be unable to completely grasp this one. I can get one step and I'm not even sure that it's right.
    [tex]y(6-10e^x) = 3-4e^x[/tex]

    After that I'm stuck. I can't seem to isolate e. Either I'm misunderstanding the law of logarithms or I just don't know. If someone could point me in the right direction, it would be greatly appreciated.
     
  2. jcsd
  3. Jan 5, 2012 #2
    Try using this :

    [itex] log(y) = log \left(\frac{3-4e^x}{6-10e^x}\right)[/itex]
     
  4. Jan 5, 2012 #3
    So my next step would be to simplify the right side using log laws, yes?
    [tex]log(y)=log(3-4e^x)-log(6-10e^x)[/tex]

    This seems wrong but it's the only way I know.
     
  5. Jan 5, 2012 #4

    Mark44

    Staff: Mentor

    I don't see that this is a helpful hint.
     
  6. Jan 5, 2012 #5

    Mark44

    Staff: Mentor

    Multiply out the left side, and then move all the terms with ex to the left side, and all the other terms to the right side. Finally, factor out ex and isolate it.
     
  7. Jan 5, 2012 #6
    Ah I see it now. Don't know how I missed that before. Thanks for the help mark!
     
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