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Can anyone help me solve this for $x$:

$y= x \cdot 2^x$

I know for $y= 2^x$, that $\log_2(y) = x$

And I can get $\displaystyle \frac yx = 2^x \implies \log_2 \frac yx = x $

But I can't condense to only a single $x$ in the equation.

N. F. Taussig
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David
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    https://en.wikipedia.org/wiki/Lambert_w_function –  Apr 04 '16 at 22:22
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    This question has been asked so many times and answered equally many times with a link to the Lambert W-Function wiki page. How can you not have seen this before asking the question? – Edward Evans Apr 04 '16 at 22:27

1 Answers1

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ProductLog(y) is the answer. Google further to read further about its differential equation, series expansion etc.

Narasimham
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