The log files will only be removed automatically when the backup record itself is removed. If you are okay with the backup record being removed from the database, the option in the backup profile's Configuration page you're looking for is called Obsolete Records To Keep.
There is a reason for this. Log deletion and file deletion are very different things. If you have a problem it does help having the log of the last known good backup even if you no longer have the backup archive files themselves. When you delete the backup record, though, it definitely means you are done with this backup attempt; you don't want the software to even remember it exists, which makes log files redundant by definition.
Alternatively, you can set up a CRON job using the standard Linux command find to delete log files based on their age (how long ago they were created). The command line would look like this:
find /home/example/public_html/administrator/components/com_akeebabackup/backup -type f -name '*.log.php' -mtime +30 -delete > /dev/null 2>&1
The /home/example/public_html/administrator/components/com_akeebabackup/backup part is the absolute filesystem path to your backup output directory.
The +30 part is the minimum age of the files, in days. The + in front is mandatory. +30 means "anything that 30 days old or even older".
Nicholas K. Dionysopoulos
Lead Developer and Director
🇬🇷Greek: native 🇬🇧English: excellent 🇫🇷French: basic • 🕐 My time zone is Europe / Athens
Please keep in mind my timezone and cultural differences when reading my replies. Thank you!