Seems to be a sort of 'gray' area with booking out as with logging landings and takoffs.
I regularly 'booked out' at the 'international' airport where I did my initial but I was PuT except for solo flights - so does 'booking out' mean the person doing it is in command?
Can one switch command during a flight and just log an hour of a 2 hour flight with no take off or landing? There would appear to be no legal reason to prevent it.
Secondly, as far as I can tell there is no requirement to log the number of take offs and landings - just the one of each for each line in the logbook as its assumed you have to do one of each.