Database Log File Size Growth So Huge Unexpectedly
Full backup doesn't clear the logs, I suppose your database is not in simple recovery mode as logs are increasing and its filling up rapidly. Do you take transnational log backup anytime in a day or week? 

Ideally Full backup should be taken every day, Differential backup few times in a day and log backup few times in an hour however it also depends upon RPO and RTO.

One thing to note here is transaction log backup helps you in storing active part of transaction as illustrated below:


  A transaction log backup allows you to backup the active part of the
  transaction log.  So after you issue a "Full" or "Differential" backup
  the transaction log backup will have any transactions that were
  created after those other backups completed.  After the transaction
  log backup is issued, the space within the transaction log can be
  reused for other processes.  If a transaction log backup is not taken,
  the transaction log will continue to grow.


Please read recommendation from Microsoft on backup and frequency:


  A database administrator typically creates a full database backup
  occasionally, such as weekly, and, optionally, creates a series of
  differential database backup at a shorter interval, such as daily.
  Independent of the database backups, the database administrator backs
  up the transaction log at frequent intervals. For a given type of
  backup, the optimal interval depends on factors such as the importance
  of the data, the size of the database, and the workload of the server.
  For more information about implementing a good strategy, see
  Recommendations in this topic.


You may read more about RPO and RTO from this link as nicely explained by Mr. Paul Randal.

You may also check best practice for Transaction log autogrowth and other details:

https://www.sqlshack.com/sql-server-transaction-log-administration-best-practices/