Solution of a Simple Exponential Equation via the Lambert W Function

How to solve

\begin{equation}
x = \mathrm{exp}\left(\frac{2}{x}\right)
\end{equation}
was posed at Mathematics Stack Exchange.

To solve it, we use the Lambert W function.
\begin{equation}
1 = \frac{1}{x} \mathrm{exp}\left(\frac{2}{x}\right)
\end{equation}
\begin{equation}
2 = \frac{2}{x} \mathrm{exp}\left(\frac{2}{x}\right)
\end{equation}
\begin{equation}
\mathrm{W}(2) = \frac{2}{x}
\end{equation}
\begin{equation}
x = \frac{2}{\mathrm{W}(2)} \approx 2.34575
\end{equation}
Where \(\mathrm{W}(z)\) is the Lambert W function.

A good tutorial can be found here, where we see that for \(a=b\mathrm{e}^{b}\), we have \(b=\mathrm{W}(a)\).

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