Two-logarithm matrix model with an external field

We investigate the two-logarithm matrix model with the potential $X\Lambda+\alpha\log(1+X)+\beta\log(1-X)$ related to an exactly solvable Kazakov-Migdal model. In the proper normalization, using Virasoro constraints, we prove the equivalence of this model and the Kontsevich-Penner matrix model and construct the 1/N-expansion solution of this model.