Firewall Filter match logging

When a filter rule matches a packet, and it is logged, is there a way to see under which rule it matched?

I am running my first new RouterOS router for the last 24 hours. I am watching the firewall log, and I want to make sure that my rules are not too strict.

Not directly. You can duplicate the rule in question (or rules in question), change the action to LOG and make sure the LOG version of the rule comes before the non-log version. That will log the match for that particular rule.