This paper proposes a task-space impedance controller using the dual quaternion logarithm, combining the translation and rotation impedance in a single mathematical structure. The controller is composed of an outer loop impedance controller to impose a desired apparent impedance to the robot and an inner motion control loop to ensure trajectory tracking of the end-effector pose. Experiments showing the effectiveness of the controller were run on a KUKA LWR4+ robot with a force/torque sensor in the end-effector.