"Running a full backup will normally consolidate the transaction logs on a MS database (SQL, Exchange, etc) server. If you run incremental or differential backups, it doesn't."
I'm more used to Informix where you back up the logs separately. Also the restore of a full backup plus incremental takes you to a fully check-pointed position. You only need the logs since the last incremental was made to roll forward from there. And you were doing your incrementals every night or even more frequently, weren't you?