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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...2012-05-27
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    Note that $2^2=2\times 2$. But there is another solution.2012-05-27
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    http://en.wikipedia.org/wiki/Lagrange_inversion_theorem see for a power series solution2012-05-27
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    Lagrange inversion theorem is still not able to do this question.2012-05-30
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    Another real solution is about $0.346323362278580922$2017-01-08

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