A log book is a "Personal Log" it must contain what the ANO (Art 35 requires for the purpose of obtaining or maintaining a licence. It can also include anything else the holder wishes to put in it because it is the owners personal log and there is no specified format.
Log book fraud when associated with the obtaining or maintaining a licence currently runs at about £300 a line in fines in the UK Courts, if you make an illegal claim, and once convicted you can stand to loose the licence as an unsuitable person!