There is no log for scheduled events, unless they throw exceptions... in which case, you'll find an error written to the standard MySQL "hostname.err" error log. If there isn't an error, and they aren't still running, then they processed. Each event gets a new thread id in the processlist each time it fires and the thread is destroyed when the event is done.
One option you could use is creating a table for the purpose, and inserting log entries into that table from within the body of the event, or the procedure that the event calls.
Inside a running event, the CONNECTION_ID() function returns the id of the thread where the event is running, and you can use this function in queries that do your logging, if that's useful, such as inserting a log entry including that value when the event starts, and updating that log entry when the event is almost done.
Another option is a bit of a hack (some would say), but it also works -- you can generate a "warning" in the MySQL error log from within the event or procedure fired by the event by raising a SQL warning at the end of the event. Note that this only writes to the error log from within an event, and that's because there is no client connected.
SIGNAL SQLSTATE '01000' SET MESSAGE_TEXT = 'hey, this job ran';
On some of my systems where the MySQL error log is monitored by an external process "tailing" the error log file, I have scheduled events whose only purpose is to write a warning like this to the error file periodically, so that the external process never goes more than so many minutes without seeing "something" in the often-quiet error log, to keep it happy that it is properly seeing the correct log file growing.