Thread: 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.

If you differentiate, you get this DE, which is solvable in terms of the product log function:

Link to solution.

Thank you!

You're welcome. Have a good one!