but a log? I guess I can, but what do they actually want?
Regular fuel checks are likely to be the first indication you get of abnormal consumption or a fuel leak. A fuel leak within the engine cowls probably won't be visible, unlike a hole in the wing! Most leaks are inside, coupling and fuel line failure etc.
On simple flights just pick the one quarter, one half and three quarter points or, if more convenient, waypoints, for a flight of one hour or less, just the half way point should do it. A Top of Descent check is quite a good idea too, confirmation that you have enough fuel to land or divert etc. Strong and unscheduled headwind and you may have to pick a closer diversion.
Logging fuel at start and landing gives you consumption and this may be useful to the engineers for engine performance monitoring.