Logarithmic relaxation is a unique relaxation process exhibited by a few molecular liquids and biomolecules. However, the microscopic origin of logarithmic relaxation is still unclear. To understand the origin of this process, we studied two liquids that exhibit logarithmic relaxation in a dissolved state using quasielastic neutron scattering (QENS) and depolarized dynamic light scattering (DDLS). Although the intermolecular potential of the liquids is drastically different in the dissolved state from the bulk liquids, we observed that the logarithmic relaxation still persists. Our results indicate that the intermolecular potential does not play a role in determining the logarithmic relaxation process. The coupling of rotational and translational relaxation processes could be the origin of the logarithmic relaxation process exhibited by the molecular liquids.