How to find point of intersection between quadratic and exponential equation How can I find the point of intersection between a function like $2^x$ and $x^2$?
I know you have to equate them but I don't know what to do after that.

The equation : $2^x=x^2$ has two obvious soutions for $x=2$ and $x=4$.
We can verify that for $x>4$ the two function $f(x)=2^x$ and $g(x)=x^2$ are such that  and $f'>g'$ so they have no other intersections for $x>4$.
For $-1\le x \le 0$ we can see that $f(-1)=1/2$, $g(-1)=1$, $f(0)=1$ $g(0)0$, so, since the two function are contiuous in this interval , there is atleast one other solution between $-1$ and $0$, and an inspection to hte graph of the two function confirm that there is a unique solution that is near $x=0.766..$
