To solve the equation 2^x = x^3, we can start by graphing the two functions and finding their intersection point.

Graphing the function y = 2^x and y = x^3, we can see that they intersect at x ≈ 1.5.

To solve the equation x^50 = x, we can rewrite it as x^50 - x = 0. Factoring out an x, we get x(x^49 - 1) = 0. This equation is satisfied when x = 0 or when x^49 - 1 = 0.

Solving x^49 - 1 = 0, we find that x = 1 is a solution. However, x = 0 is also a solution.

Therefore, the solutions to the equations 2^x = x^3 and x^50 = x are x = 0 and x = 1.