For about a year, I've had this problem in my head. It stemmed from a very benign hypothetical sci-fi scenario, which I won't bother repeating, as it is unimportant next to the conundrum that resulted.(adsbygoogle = window.adsbygoogle || []).push({});

x^x=c is interpreted as a single variable located in both the base and the exponent, set equal to a constant (whether it be something as incredibly easy as 4, wherein x=2, or as mind-numbingly difficult as 3 [which was the problem -- x^x=3]). I don't even know what branch of mathematics to use to solve this deceptively simple problem. Anyone want to take a crack at it, or at least point me in the right direction?

Yes, I'm aware one can plug-'n-pray, or just stick it in a graphing calculator. What I'm asking is whether there's an algebraic method to solve it, or if it's an unsolved problem.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# X^x = c

**Physics Forums | Science Articles, Homework Help, Discussion**