You can tell the system what activities you want to track. I'd highly recommend only tracking activities you are actually using.
Settings > On-line marketing > Contact management > Activities
Secondly, I'd recommend making sure the delete inactive contacts task is running. Keep in mind it will only delete 1000 contacts per day. So it may take quite some time to clean that up.
Lastly, depending on the need for transactional database backups, you may want to change your database's recovery model to Simple vs. Full. This will help with the log file size.