Electrical transport in the pseudogap region of cuprate superconductors is known to follow an exotic log(1/T) temperature dependence, either at very high field or at very low doping. Whether this implies an insulating ground state from which superconductivity arises, or can be distinguished from vortex flux flow at all, is an intriguing question. Working deep within the superconducting phase, we take a different approach and measure the response of vortices to microwave-frequency driving currents. We found that flux-flow resistivity follows a similar log(1/T) temperature dependence across the entire superconducting phase. This include a regime at high carrier dopings where the normal-state transport is Fermi-liquid-like, indicating that the log(1/T)temperature dependence is a dynamical property of the vortices themselves. Analysis on vortex viscosity spectrum suggests that this exotic log(1/T) temperature dependence is intimatedly related to nodal quasiparticle dynamics outside the vortex core, in sharp contrast to the case in conventional superconductors.