never had the IRS question this but if they did they would look at the following items (not all inclusive)
place of employment
address listed on your federal and state returns, driver's license, vehicle registration, voter registration
location of your banks, religious organizations and recreation clubs with which you are affiliated
financial records
utility bills
testimony of neighbors
also vacation or other short absence counts as time you lived at home
you are committing perjury if you lie.
i have never heard of a person keeping a log probably because its self-serving