In this work, the exact solution to the mean value theorem (MVT) problem applied to the maximum power point (MPP) calculation is presented, besides an improvement to this solution is developed based on an expression of the MPP that depends on the optimal load and the characteristic parameters of the photovoltaic (PV) module. Both approximations depend only on the natural logarithm, avoiding the evaluation of the W function. The validation of the approximations is performed by comparing them with real measurements and the numerical solution of the 5-parameter single diode model (SDM) using dataset from 11 commercial modules and 6 different technologies, as well as by comparing them with existing approximations in the literature..