9^x=2e^x^2 solve for x?

Answer 1

take the natural log of both sides:

ln(9^x) = ln(2e^(x^2))
xln(9) = (x^2)ln(2e)
0 = (x^2)ln(2e) - xln(9)
0 = x(xln(2e) - ln(9))

first case:
x = 0
second case:
(xln(2e) - ln(9)) = 0
x = ln(9)/ln(2e)
x = approximately 1.2977

Answer 2

That looks awfully advanced for American schools...

Are you sure you meant ^ and not * ?

The way you have it written, it is 9 to the power of x equals 2e to the power of x squared.