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Does this equation have any solution?

  1. Mar 9, 2005 #1
    [tex]x\multsp =\multsp {{e}^x}[/tex]

    I'm aware there's no real solution, but does any complex solution exist?
     
  2. jcsd
  3. Mar 9, 2005 #2

    dextercioby

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    Yes,it has 2 distinct solutions:

    [tex] x_{1}=-W(-1) [/tex]

    [tex] x_{2}=-W(-1,-1) [/tex]

    ,where W is the Lambert function.

    Daniel.
     
  4. Mar 9, 2005 #3
    I see. Having read a bit about the Lambert function on Http://www.mathworld.com it doesn't make much sense to me.

    Is the following value:

    [tex]x_{1}=-W(-1)[/tex]

    ...a complex number, or something entirely different?
     
  5. Mar 9, 2005 #4

    dextercioby

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    You mean a # of nonzero imaginary part...?Yes it is.As u said and as a graph and elementary calculus would show,for real #-s the equation does not have solution.

    Daniel.
     
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