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How to solve this equation

  1. Jun 23, 2013 #1


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    I know we can solve e^x=x by the Lambert W function, but is it possible to solve the following equation:


    in terms of a, b, and c.
  2. jcsd
  3. Jun 23, 2013 #2

    Simon Bridge

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    Welcome to PF;

    Solving for x given a,b,c you mean? That would be the intersection of a line with a quadratic in e^x... that is $$ e^{x}\left ( e^x - 1\right ) = mx+k$$ ...where ##m=-b/a## and ##k=c/a##.
    And you want to find x given m and k.
    That help?
    Last edited: Jun 23, 2013
  4. Jun 23, 2013 #3


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    Thank you Simon. Yes. I am wondering if there is some special function can solve this problem, i.e. given the values of a,b,c (or m,k in your equation) I can find out the value of x without looking at the graph.
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