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Math Help - Unknown Solution to Equation involving Natural Logarithm

  1. #1
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    Unknown Solution to Equation involving Natural Logarithm

    Hello,

    I am looking for a solution, i.e. f(x) (most likely complex), to the equation

    Ln(f(x))/f(x) = x

    Having scanned through logarithm literature, I have not come across this equation. Would anyone here happen to know its solution?

    Thank you.
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  2. #2
    A Plied Mathematician
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    If you differentiate, you get this DE, which is solvable in terms of the product log function:

    Link to solution.
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  3. #3
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    Thank you!
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  4. #4
    A Plied Mathematician
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    You're welcome. Have a good one!
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