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. 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.