TITLE: Lambert- W -Function calculation?
QUESTION [12 upvotes]: I have  an equation of the form:
$$  n \log n = x $$
Upon searching I came across the term  "Lambert- W -Function" but couldn't find a proper method for evaluation, and neither any computer code for it's evaluation. 
Any ideas as to how I can evaluate?

REPLY [3 votes]: Although this has already been answered, I think a step by step explanation is more informative than a general one. 
The following is my attempt:
\begin{align*}
n \ln (n) =x \quad & \Rightarrow \quad \ln n^n=x \\
 & \Rightarrow \quad n^n=e^x \\
 & \Rightarrow \quad n=e^{x/n} \\
 & \Rightarrow \quad n \times \frac{x}{n}=\frac{x}{n}e^{x/n} \\
 & \Rightarrow \quad x=\frac{x}{n}e^{x/n} \\
 & \Rightarrow \quad W(x)=W \left(\frac{x}{n}e^{x/n} \right) \\
 & \Rightarrow \quad W(x)=\frac{x}{n} \\
 & \Rightarrow \quad \boxed{n=\frac{x}{W(x)}} \\
& \Rightarrow \quad n=\frac{x}{x/e^{W(x)}}  \quad \text{(since 
 $W(x)e^{W(x)}=x$)}\\
& \Rightarrow \quad \boxed{n=e^{W(x)}} \\
\end{align*}