Monitor Logs and email with activity?

I have a server with a faulty power button that likes to reboot itself. Usually there are warning signs, like the acpid log file in /var/log starts spamming garbage for about 10hrs or so.

Is there an easy way I can have something monitor the acpid log and email me when it has new activity?

I wouldn't consider myself extremely advanced so any "guides" you may have for accomplishing something like this would be very helpful and much appreciated. Thank you!