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Solve For It

  1. Apr 2, 2003 #1
    Problem 1:

    e^-x = x

    Solve for x.


    Problem 2:

    x^y - y^x = xy - x - y

    Solve for y.
     
    Last edited by a moderator: Apr 2, 2003
  2. jcsd
  3. Apr 2, 2003 #2

    HallsofIvy

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    Neither of these have "elementary" solutions (solutions in terms of the "elementary" functions: polynomial, rational, trig, log, exponential).

    The first can be solved numerically or they can be solved in terms of the "Lambert W function".
     
  4. Apr 2, 2003 #3
    Problem 1:

    e^-x = x
    e^x = 1/x
    x e^x = 1
    x = ProductLog(1), where ProductLog (a.k.a. Lambert's W-function) is defined as the inverse of f(W) = W e^W

    Numerically, the answer is about 0.567143290409784

    Problem 2:

    I don't know. Sorry.
     
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