This is an old topic, but I'm posting here so that if someone else does a Google search, they'll find the answer.
This behavior is most likely caused by the outbound firewall HandsOff!, in versions of OS X prior to 10.8.4.
I had this very same problem under 10.8.3, and was only able to stop it by uninstalling HandsOff!
After upgrading to 10.8.4, I re-installed HandsOff! to see if anything had changed.
Sure enough, the constant logging has stopped.