Shared and Reseller
You do not have access to the email logs for your account. Please email support@hostgator.com to request a copy of the logs we have. Please note that we do not keep the logs for more than a few days, so our logs will be limited.
VPS and Dedicated Server
On a Dedicated Server or VPS, the email log files are located in the /var/log/exim_mainlog directory.
The email login attempts are logged in the /var/log/maillog directory.