Luxembourg - A Nice Math Olympiad Exponential equation| Find X

An amazing math Olympiad Exponential Problem
Find unknown variable X
In this tutorial i am going to solve an amazing math Olympiad Exponential question contain unknown variable X. Could you find X

[@sy8146]

Thank you for explaining. My answer is x = -1, 1. If x=-1, left side is (-1)^(-1) [= (-1)^(odd number) ] = -1 (= right side). Thus, -1 can be one of the solutions.

[@walterwen2975]

x^x = x, (x^x)/x = 1, x^(x - 1) = 1 = x^0; x - 1 = 0; x = 1