Log files on cPanel servers are not stored at the same location of the default OS installation. The locations of common log files are shared below.
Apache
Apache is the web server that is typically utilized by cPanel. On cPanel servers Apache does write to a rather high number of logs as each site has its own traffic log.
/usr/local/apache/logs/access_log
The access_log is used to log all http requests received. These requests can be valid or invalid. All of this gets logged in the access_log file.
/usr/local/apache/logs/error_log
On cPanel servers all Apache errors, regardless of site, are logged in the error_log file.
/usr/local/apache/domlogs
Within the domlogs folder each site on the server will have its own log file. These files will be the fully qualified domain name for the domain, ie abc.com, xyz.com. All http traffic to a site will be logged in this log file.
Exim
Exim is the MTA(Mail Transfer Agent) that cPanel utilizes. Exim has three primary logs, but only two of these logs contain useful information
/var/log/exim_mainlog
The exim_mainlog contains ALL interactions that exim handles, so both incoming and outgoing mail transactions.
/var/log/exim_rejectlog
The exim_rejectlog contains all connection attempts that were denied. This information is also logged in the exim_mainlog.
cPanel
cPanel does log all http traffic to WHM, webmail, and cPanel access. All cPanel logs are located in the /usr/local/cpanel/logs directory.
/usr/local/cpanel/logs/access_log
This access_log contains all traffic to WHM, cPanel, and webmail over http.
/usr/local/cpanel/logs/error_log
This error_log contains all errors that occur when accessing a cPanel related site over http or https.
FTP
Regardless of the FTP server you use, cPanel logs all connections, uploads, and downloads into the system messages log file located at
/var/log/messages
All FTP transactions are recorded in messages. This file also has a lot of other messages with the FTP transactions.
MySQL
The MySQL log will contain all actions related to start/stop/restart of the service along with errors if any.
/var/lib/mysql/hostname.err