Thank you for information. It seems that our logs are too big...
We are facing this issue: https://tracker.moodle.org/browse/MDL-56223
If I go to random old course with assignments, with no students, and go to Report > Logs, I see that "Calendar event updated" is running everyday, multiple times per day, so it generates ton of logs and stores in mdl_logstore_standard_log table.
Would it be safe to run sql query in phpmyadmin and delete "Calendar event update" records from mdl_logstore_standard_log table?
This issue is still unresolved. I will try to post about this issue in forums, maybe someone faced this issue and has a solution.
The log table is mainly used to track details of what has been done, and be able to browse (or search) it. It can also be used to generate statistics (if enable). So, no problem to delete things in it !
Moreover deleting "abusive" information isn't a problem but better cleaning unwanted things.
I think, seeing people facing this problem, and knowing problems generated (big logs, big backups, too much time and disk needed...), that it's worth doing things to have it resolved (soon).