I think he just means to get to know each other better.. like outside of wlo.
You know what a logbook is right?

Think of it as a journal and every day or so you write something in it. Usually you would put the day, month and year in it so that's what you do here and all he is saying is to put stuff down for the day like how he has a math exam tomorrow (good luck with it by the way!)

It can really be anything as long as you don't include any really personal info or anything that will cause problems.

e.g. you can say you got a pet, had a sweet party, watched a new insanely cool movie etc.

So yea... that's what I think he's trying to get us to do here...