Show that the equation 3x x2 has at least one solutionSolut

Show that the equation 3^x = x² has at least one solution.

f(x) = 3^x - x^2 is continuous and f(-1) = -2/3 and f(0) = 1. Since these are of opposite sign f(x) must have a zero (by the intermediate value theorem) between -1 and 0 and so your equation has a solution in the interval [-1,0].