  I consider the Hermitean two-matrix model with a logarithmic potential which
is associated in the one-matrix case with the Penner model. Using loop
equations I find an explicit solution of the model at large N (or in the
spherical approximation) and demonstrate that it solves the corresponding
Riemann-Hilbert problem. I construct the potential of the Kazakov-Migdal model
on a D-dimensional lattice, which turns out to be a sum of two logarithms as
well, whose large-N solution is given by the same formulas. In the "naive"
continuum limit this potential recovers in D<4 dimensions the standard scalar
theory with quartic self-interaction. I exploit the solution to calculate
explicitly the pair correlator of gauge fields in the Kazakov-Migdal model with
the logarithmic potential.
