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Math Help - Solving Equation (Exponential)

  1. #1
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    Solving Equation (Exponential)

    I need to solve:
    \frac{1}{x} e^{-\frac{3}{x}} = 0.1086

    My method:
    \frac{1}{x} e^{-\frac{3}{x}} = 0.1086
    e^{-\frac{3}{x}} = 0.1086x
    \ln \left(e^{-\frac{3}{x}} \right)= \ln (0.1086x)
    -\frac{3}{x} = \ln (0.1086) + \ln (x)

    But I'm stuck from here. Don't understand what to do.
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  2. #2
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    I seriously doubt that you will be able to find an exact value for \displaystyle x. Just use a numerical method and/or some technology.
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  3. #3
    Super Member TheChaz's Avatar
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    From the first line, multiply both sides by -3.
    Then you'll be in a form where you can use...
    Lambert W function - Wikipedia, the free encyclopedia
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