As the graph shows, the only other possible solution is x = 0. But as $\displaystyle 0^0$ is not defined, it can't be 1. Thus there are no other solutions.
As the graph shows, the only other possible solution is x = 0. But as $\displaystyle 0^0$ is not defined, it can't be 1. Thus there are no other solutions.
-Dan
Alternatively, $\displaystyle x^x = 1 \Rightarrow x \ln x = 0$.
Therefore x = 1 or x = 0. But as topsquark has quite rightly pointed out .......