It is hard to be sure. The meaning is not obvious. A "log" can mean a detailed record of events, with dates and times to the minute. For centuries, ships' captains have kept logs. 10 o'clock, sighted whale. 11 o'clock, changed course. 12 o'clock, took noon sight, latitude 50°S. A "log" can mean a record of when people enter and leave a building. When you visit an office building, you may have to sign a log at the front desk. You will write your name and the time you entered, and then when you leave, the time you left. It sounds as if there is some kind of "house log." Perhaps there is a security system protecting the house. Perhaps it keeps a log, a record, of when people enter and leave the house. The father can read the log and find out when the narrator got home.