A method is given for solving logarithmic potential problems in which the potential is preassigned over part of the boundary and the normal derivative over the remainder. A ``mixed'' Green's function is defined such that it vanishes over part of the boundary of interest and its normal derivative vanishes over the remainder, and the solution for the logarithmic potential is expressed in terms of this function and the boundary conditions by means of Green's theorem. Taking the case of the infinite quadrant as the ``prototype'' region the solutions for other regions such as the infinite half plane, infinite and semi‐infinite strips, and the circle are obtained by mapping them on the infinite quadrant; these are illustrated by several specific examples.