It might be better to view /var/log/exim_mainlog to see if the mail was sent properly. If so, I would check and see if that log shows any errors about the delivery. If you aren't seeing the message generated at all, you may want to confirm the notifications are setup and that your disk usage is meeting the requirements for the message to be sent.
Most of the system log files would need to be checked using an SSH connection. If you aren't familiar with using SSH, our article here would be a good place to start:
support.cpanel.net
How to log into server using SSH?
The SSH network protocol allows you to connect to another web server over the Internet via a command line interface (CLI). You can use this network protocol to remotely manage your server, config...