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Math Help - solve ln x = x - 2 for x

  1. #1
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    solve ln x = x - 2 for x

    I can't figure it out. =/

    ln(x) = x - 2
    x = e^{x - 2}

    x = \frac{e^x}{e^2}

    I'm quite stuck. I feel like I should know how to do this, but just can't remember. >_<
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  2. #2
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    e^(i*pi)'s Avatar
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    You need to solve it numerically I'm afraid. Plotting it gives rough ideas of x= 0.16 and 3.13
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  3. #3
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    How irksome. Thanks though.... >_< I detest having to use Newton's method.
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  4. #4
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    Quote Originally Posted by Zizoo View Post
    How irksome. Thanks though.... >_< I detest having to use Newton's method.
    Use the Bisection Method then :P
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  5. #5
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    Quote Originally Posted by e^(i*pi) View Post
    You need to solve it numerically I'm afraid. Plotting it gives rough ideas of x= 0.16 and 3.13
    Can be solved in closed form in terms of Lambert's W function (real (0) branch for a real solution):

    x=-\text{W}(-e^2)=0.158594

    CB
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