The reg says:
(h) Logging training time. (1) A person may log training time when that person receives training from an authorized instructor in an aircraft, flight simulator, or flight training device.
(2) The training time must be logged in a logbook and must:
(i) Be endorsed in a legible manner by the authorized instructor; and
(ii) Include a description of the training given, the length of the training lesson, and the authorized instructor's signature, certificate number, and certificate expiration date.
However there is no definition of logbook. If pressed the FAA will admit if you have a stack of beer coasters with all the required information on them you're good to go.