Roughening transitions are often characterized by unusual scaling properties. As an example we investigate the roughening transition in a solid-on-solid growth process with edge evaporation [U. Alon, M. Evans, H. Hinrichsen, and D. Mukamel, Phys. Rev. Lett. 76, 2746 (1996)], where the interface is known to roughen logarithmically with time. Performing high-precision simulations we find appropriate scaling forms for various quantities. Moreover we present a simple approximation explaining why the interface roughens logarithmically.