Reconditioned for your Smath tool box.
Ready to use from Maple => Lambert[,,,]

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Lambert ProductLog.sm (30 KiB) downloaded 122 time(s).

... generally, LambertW is not clearly understood.
LambertW is not a function, it is a "function solution"
of which the argument is the solution that you plug in W(x).
Working with Lambert is working in the "domain solution",
something like working in Laplace, Fourier, Hilbert ... domain.
Laplace, Fourier after working in their "transform algebra"
they are inversible. Lambert is: done/bingo.

... final brew for Smath.
In many examples of solving algebraic expressions this version
will simply fail because of the simple Lambert branch is available.
In short: a very poor parent compared to Mathcad 11 .

Jean

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Lambert ProductLog.sm (101 KiB) downloaded 94 time(s).

Thank you Jean for this post about LambertW function,

Although my colleagues from pharmacology and enzymology fields are not using Lambert W in their teaching, just recently I found that it attracted many researches from enzymology (your first example and unavoidable Michaelis-Menten equation types)

Regards,
Radovan