I'm not sure where to start on these two problems, so any help is greatly appreciated.
1)4^x = x^2
2)5-x^2 = e^x
I suggest a numerical approach, namely graph each side of the equation, and from the intersection point(s), do successive approximation using Newton's or other methods.
For (1), x=-0.64 approx., and for (2), there are two solutions, at x=-2.2 and x=1.3 approx.