An Econ 11 student is solving a partial equilibrium question which gives a utility function U (x, y) =x1/2y1/2 and a production function F (K, L) =K1/2L1/2. They think it would be easier to solve if they took logs of each function and multiplied by 2 to get U(x, y) = ln(x) + ln(y) and F (K, L) = ln(K) + ln(L). Can they do it? Explain. (Complete answers should touch on the validity of each transformation).