It is implicit in current theories that compare simulation and analytic computation to assume the long-range electrostatic force in electrolyte solutions is an exponential function of separation with a decay length equal to the Debye screening length. Theory, recently verified experimentally, shows that the decay length of the asymptotic form of the double-layer force in mixed and asymmetric electrolytes is markedly different from the classical Debye length. We derive the full (analytic) asymptotic form of the radial distribution function for electrolyte mixtures and extend the result to mixtures of symmetric and asymmetric electrolytes. This allows a simple and accurate determination of the activity and osmotic coefficients of dilute mixed electrolyte solutions.