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Math Help - Solving this eqn?

  1. #1
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    Solving this eqn?

    Hi,

    I'm not quite sure how to tackle this equation:

    -x=lnx

    How do I solve for x? All I know is there is one real value of x, and that is ~.567. Is there a tidy expression for x, and if not, is there a name for this occurrence, or even this type of eqn?

    Thanks,
    B
    Last edited by fwlksajzxlc; March 20th 2009 at 02:15 PM.
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  2. #2
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    Quote Originally Posted by fwlksajzxlc View Post
    Hi,

    I'm not quite sure how to tackle this equation:

    -x=lnx

    How do I solve for x? All I know is there is one real value of x, and that is ~.567. Is there a tidy expression for x, and if not, is there a name for this occurrence, or even this type of eqn?

    Thanks,
    B
    -x = \ln x \Rightarrow e^{-x} = x \Rightarrow 1 = x e^x.

    Therefore x = W(1) where W is the increasingly well known Lambert W-function (eg. see Lambert W-Function -- from Wolfram MathWorld. You can search MHF for various other questions where it's been used.)
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  3. #3
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    Thank you mr fantastic.

    B
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