An exact solution to the Poisson-Boltzmann equation is proposed with the assumption of a new potential of mean force. As a possible candidate for this purpose, a logarithmic potential of mean force changes the non-linear differential equation to a linear one, while achieving the same results as those with the original Debye-Huckel theory. The effect of dielectric saturation is discussed with respect to the radial distribution function. From the proposed potential function, a simple perturbed equation of state for a non-primitive model was developed using statistical mechanics and other equations to derive the activity and osmotic coefficients. These equations correspond to the Lewis-Randall framework. The problem of deriving a closed form for the compressibility factor is bypassed using an approximate function. The present work is compared with the original Debye-Huckel (DH) theory and the mean spherical approximation (MSA) theory using the simulation data of activity coefficient for restricted primitive 1:1, 2:1 and 2:2 electrolyte systems. Individual ionic activity coefficient data from aqueous NaCl solution at 298.15 K were examined with our proposed theory, with which the results including other thermodynamic properties were in better agreement with the experimental data than were those from DH and MSA, especially for high-valent ions. Two model parameters for each ion were used at a fixed temperature and an additional parameter was needed for variable temperatures. The use of closed equations for thermodynamic properties of electrolyte solutions should foster research examining electrolyte solutions for increased thermodynamic accessibility. (C) 2012 Elsevier B.V. All rights reserved.