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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- Jan 6th 2011, 02:53 PMKrayzBluUnknown 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. - Jan 6th 2011, 03:53 PMAckbeet
If you differentiate, you get this DE, which is solvable in terms of the product log function:

Link to solution. - Jan 6th 2011, 04:59 PMKrayzBlu
Thank you!

- Jan 6th 2011, 07:56 PMAckbeet
You're welcome. Have a good one!