A Tricky Exponential Equation e^(x)=ln(x) | Lambert W Function | Math Olympiad

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In this math algebra video, we shall solve a very nice exponential equation e^(x)=ln(x) by applying the rules of exponents, natural logarithms, and the lambert W Function. This question was taken from Mathematics Olympiad.
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hi friends. hi teacher

We know that W(xlnx) = lnx

And how about *W[(lnx)/x]* ?
Is there some "formula" in this case?

For example
We know W(17ln17) = ln17

But to find/calculate W[(ln17)/17], can we find an exact value, a perfect value, without using approximations, without using things like Wolfram Alpha?

SidneiMV
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The problem does not make sense at all. Generally speaking, for such a problem, it is common sense that we do solve the equation for "Positive Real numbers x.
If you really want us to solve the problem, you should ask us, you should wite : Sove in complex numbers e^x = Ln x.

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