Microsoft's Remote Desktop Protocol does not, on its own, have activity logging capabilities. Event logs on a remote computer do, however, log RDP connections to that computer, but the activities performed during the RDP session are not recorded.
RDP is a way for individuals to access computers remotely and use them as though they were sitting directly in front of them. Because RDP merely facilitates the remote communication between two computers, it does not log any activity that occurs over the connection. Other, third-party remote viewing tools do offer logging capabilities. Additionally, activity may be logged directly on the remote computer using any number of third-party programs that record information such as keystrokes, which programs are accessed and what files are opened.