See part 61.420 then read 61.340.
Nav log per CAR 78 as was mentioned. I refer your later comment about some stuff being good to do and my opinion is that a fuel log is definitely one of those.
Yep, they seem to have written it as if Part 91 was imminent - well, it was imminent at one time. But don't you worry, when Part 91 comes out it will have all of this stuff in it - , fuel log, W&B calcs for every flight to be carried with you, carry copies of weather forecasts and NOTAMs etc to prove that you got them etc etc. Lots of worse draconian stuff in it. It will have this stuff in it unless WE push it back (as AOPA did when it was about to be implemented).