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I hope this is not too elementary a question to post on here. If so, apologies.
I'm stumped how I would solve for x where $10^{10000} = x^x$. Thanks!

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    $\begingroup$ Using common logarithm on both sides gives $10000 = x\log_{10} x$ But nothing more came to my mind. $\endgroup$ – quapka Nov 24 '14 at 19:07
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    $\begingroup$ Definitely not "elementary"! $\endgroup$ – Aryabhata Nov 24 '14 at 20:27
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You can express the solution using Lambert's W function, but in practice you'd find it numerically. Take logs on both sides to get $$ 10000 = x \log_{10}(x) $$ and use bisection or Newton-Raphson to approximate the solution.

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