# Thread: The equation

1. ## The equation

The equation

$x^x=1$

has the obvious solution x=1 find others

2. Originally Posted by perash
The equation

$x^x=1$

has the obvious solution x=1 find others
As the graph shows, the only other possible solution is x = 0. But as $0^0$ is not defined, it can't be 1. Thus there are no other solutions.

-Dan

3. Originally Posted by topsquark
As the graph shows, the only other possible solution is x = 0. But as $0^0$ is not defined, it can't be 1. Thus there are no other solutions.

-Dan
Alternatively, $x^x = 1 \Rightarrow x \ln x = 0$.

Therefore x = 1 or x = 0. But as topsquark has quite rightly pointed out .......

Note however that $\lim_{x \rightarrow 0} x^x = 1$ ......