Exim main log: /var/log/exim_mainlog
Apache access log: /usr/local/apache/logs/access_log
Apache error log: /usr/local/apache/logs/error_log
POP/IMAP logins are in: /var/log/maillog
FTP Logins are in: /var/log/messages
SSH Logins are in /var/log/secure
Mod_security log: /etc/httpd/logs/audit_log (may depend on installation)