Exim
Exim is a mail transfer agent (MTA) used on Unix-like operating systems. Exim is free software distributed under the terms of the GNU General Public License, and it aims to be a general and flexible mailer with extensive facilities for checking incoming e-mail.
Exim has been ported to most Unix-like systems, as well as to Microsoft Windows using the Cygwin emulation layer. Exim 4 is currently the default MTA on Debian GNU/Linux systems.
A large number of Exim installations exist, especially within Internet service providers and universities in the UK. Exim is also widely used with the GNU Mailman mailing list manager, and cPanel.
In March 2017 in a study performed by E-Soft, Inc., approximately 57% of the publicly reachable mail-servers on the Internet ran Exim.
Logs
The main exim log location is
/var/log/exim_mainlog
This log governs sending and receiving of email.
The main log for email account access is
/var/log/maillog
Check exim for unique email sent out
sudo cat /var/log/exim_mainlog | grep "A\=dovecot_login" | awk -F"A=dovecot_login:" {'print $2'} | cut -f1 -d' ' | sort | uniq -c | sort -n | awk {'print $1, " unique emails sent by " , $2'} | grep EMAILADDRESS