If you do not want all the backup database or backup log messages to show up in the Windows event viewer and SQL Server error log, the only thing to do is to add a trace flag to the SQL Server instance start up parameters. It is called trace flag 3226 and can be added by opening the SQL Server Configuration Manager, choosing Properties on the instance and under Startup Parameters add the string: -t3226
Then restart the instance, now the messages should not be logged to event viewer anymore.
Why do this at all you ask? Well one example can be a client of mine that has 2000 databases in an instance, the logs are filled up with messages of successfull database and log backups, can’t see the trees!