Back in the Navy, I didn’t really even have access to my logbooks. The entries were made using what we called the “Yellow Sheets”. These were turned in at maintenance after every flight. I suppose I could have gone to the squadron admin department and asked to see the logbooks. I have them now stored with other military paperwork. The hours that I fly for the airline are all done by computer. Every leg is accounted for based on ACARS times. If I want to see my block hours flown, I can just log on and click on that. It tells me every hour flown in each aircraft type, PIC time and it also gives a rundown of hours flown in the last year, six month and 90 days.
That makes a lot of sense really, especially given how regularly I'm sure they keep you flying. I'm sure they probably have some algorithm somewhere to get the most work out of you they can in your allowed hours too.