A log book is essential if you are serious about monitoring your progress. A logbook does not have to be a book, it is simply a place where you record on a per session basis what exercise you have done, how much you have lifted, how many sets you have done, your diet etc. You can put as many details as you like, even how you felt at that time, or as little details as you wish, perhaps just the date, the exercise and the maximum weight you lifted for this exercise.
What is important in a logbook is to have regular and reliable data so that you can observe the trend in your progress. Are you lifting more weight or is your workout reaching a plateau? If so, then might be the time to change exercise.
My logbook used to be a scrap of paper in my pocket containing date, exercises, sets and max weight lifted. I have many of them going back over many years and it is fascinating to refer back to them and look at my progress. After a few years, I was no longer working out hardcore because I was involved in other sports but I just wanted to keep fit. So I didn’t keep any records, instead I was listening to my body and did whatever exercise I felt like doing on that day. Instinctive training, I’ve heard it’s called.
While you might feel a great sense of freedom not to be dictated from a scrap of paper containing your programme, it is not possible to measure any progress that way. If you are already fit and work out just to stay as such, instead of getting in shape, then you can try the instinctive training. But it’s certainly not for beginners.