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

Question

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!

Answer 1

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.