# Solve $x^x=2x$ for $x$, s.t. $x\in\mathbb{C}$

Solve $x^x=2x$ for $x$, such that $x\in\mathbb{C}$.

I'm not sure if the question has a closed form solution.

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This is equivalent to $(x-1)\ln x = \ln 2$. $2$ works, but I dont know more... – guaraqe May 27 '12 at 12:12
Note that $2^2=2\times 2$. But there is another solution. – Norbert May 27 '12 at 12:12
en.wikipedia.org/wiki/Lagrange_inversion_theorem see for a power series solution – Jose Garcia May 27 '12 at 12:44
Lagrange inversion theorem is still not able to do this question. – ᴊ ᴀ s ᴏ ɴ May 30 '12 at 10:12