The classic location for log files is /var/log. Some logs are files directly in /var/log, others are located in its subdirectories.
SystemD's logging practice is different, and most distros have switched to SystemD as an init (and behind-the-scenes management and logging) system, but many distros have
rsyslog installed, which pipes SystemD logs to /var/log. I'm hardly expert in SystemD, but here's a good tutorial on SystemD logs:
https://www.digitalocean.com/communi...e-systemd-logs
If your hosting provider enables it, I'd suggest that to set up ssh access to your server so you can swoop in and use the command line to view the log files, as well as perform other maintenance functions.