We are developing a method that uses static light scattering as a non-invasive means for determining intensive free energies of n-component liquid mixtures, by solving a second-order nonlinear partial differential equation appropriate for single isotropic liquid phases. Forward light scattering efficiency data permit integration of this equation without choosing parametric free energy models in advance. With prior information about phase boundary locations, the method also accommodates phase separation. We address statistical and practical issues relevant for applying the method to experimental data.