You don't need to have a log but you do have to be able to reconstruct and retrieve information as if you do have one. As far as ID info goes, for an established deposit customer, if you have ID info on file either from your CIP efforts or from earlier ID records all you need to record is the account number, since that will lead to the ID info.
If however, your ID info is deficient, this is an opportunity to record it, keep it, and move on.
John S. Burnett
Fighting for Compliance since 1976
Bankers' Threads User #8