Logs
Unless set up otherwise with the command logging (see official documentation), bind9's error messages are directed to the default error logs (/var/logs/syslog).
The server does not respond
$ dig @mynameserver.example.com mywebsite.example.com
; <<>> DiG 9.7.3 <<>> @mynameserver.example.com mywebsite.example.com
; (1 server found)
;; global options: +cmd
;; connection timed out; no servers could be reached
It could be one of three things:
1) The nameserver (bind9) is not started. Check: