What is the exact solution for this equation? I have been thinking about this equation:
$$x^2=2^x$$
I know there is two integer solutions: $x=2$ and $x=4$. But there also is a negative solution, that is approximately $x=-0.77$.
$$(-0.77)^2=0.5929$$
$$2^{(-0.77)}=0.5864...$$
Can we find this negative solution exactly?

$x$ is a solution of the equation $x^2 = 2^x$ if :
$$\dfrac{\ln|x|}{x} = \dfrac{\ln 2}{2}$$
from the graph of the function :
$$f(x) = \dfrac{\ln|x|}{x} - \dfrac{\ln 2}{2}$$

we deduce that there are only $3$ solutions $x = 2$, $x = 4$ and $x = -0.767$.
