A continuous sequence of log backups is called a log chain. A log chain starts with a full backup of the database. Usually, a new log chain is only started when the database is backed up for the first time or after the recovery model is switched from simple recovery to full or bulk-logged recovery. 

Unless you choose to overwrite existing backup sets when creating a full database backup, the existing log chain remains intact. With the log chain intact, you can restore your database from any full database backup in the media set, followed by all subsequent log backups up through your recovery point. The recovery point could be the end of the last log backup or a specific recovery point in any of the log backups.