from sql help http://msdn.microsoft.com/en-us/library/ms186865.aspx
Under the full recovery model or bulk-logged recovery model, conventional backups also include sequential transaction log backups (or log backups), which are required. Each log backup covers the portion of the transaction log that was active when the backup was created, and it includes all log records not backed up in a previous log backup.
This indecates that the last answer is correct.
Also it would need to backup anything not backed up in a previous log backup so that it could restore to a point in time after the last log backup.