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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... –  guaraqe May 27 '12 at 12:12
    
Note that $2^2=2\times 2$. But there is another solution. –  userNaN 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

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