You might be a Sysadmin, developer, DBA or whatever, logs are like treasure boxes for anyone working in IT. And the best practice to keep logs in a central location together with local copy. Most of the logging programs have the ability to send logs to a remote logging server (as well as receive logs from remote machines); eg rsyslog , syslog-ng etc.
Read Configure TLS Encrypted Tunnel For Remote Logs Using Syslog-ng.