$ logger Hello
$ echo Goodbye | logger
$ sudo tail -2 /var/log/syslog
Feb 19 21:16:15 debian-host jander: Hello
Feb 19 21:16:21 debian-host logger: Goodbye

/var/run/user/1000/log/<app>.log
/var/run/user/1000/log/<app>/<context>.log

# /etc/logrotate.d/userlogs

/var/run/user/*/log/*.log
/var/run/user/*/log/**/*.log
{
        daily
        missingok
        rotate 7
        compress
        notifempty
        nocreate
}