Question
Where are FTP login logs?
Answer
The FTP logins are logged to the system log file. On RHEL-based systems, the system log is /var/log/messages. On Ubuntu, the system log is /var/log/syslog.
Additional resources
How to filter data from large logs in order to more easily identify problems
Why are /var/log/messages, /var/log/maillog and /var/log/secure empty?