How can I solve for x where $10^{10000} = x^x$

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!

• Using common logarithm on both sides gives $10000 = x\log_{10} x$ But nothing more came to my mind. – quapka Nov 24 '14 at 19:07
• Definitely not "elementary"! – Aryabhata Nov 24 '14 at 20:27

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.