By default, on a Linux system, the RabbitMQ log files are located in the /var/log/rabbitmq directory, like this:

ls -l /var/log/rabbitmq/
. . .
-rw-r--r--. 1 rabbitmq root  153717 Jun  8 21:20 rabbit@server001.log
-rw-r--r--. 1 rabbitmq root   60686 Jun  8 21:20 rabbit@server001-sasl.log

Or an alternate directory and log file can be be defined in the main RabbitMQ configuration file, like this (in INI format).

log.dir = /usr/local/logs/rabbitmq
log.file = rabbit.log

Here is an example of what you might find in rabbit@server001.log.

2020-09-29 15:47:24.585 [info] <0.2478.160> accepting AMQP connection <0.2478.160> (10.20.15.115:55750 -> 10.17.114.12:5671)

2020-09-29 15:47:24.630 [info] <0.2478.160> Connection <0.2478.160> (10.20.15.115:55750 -> 10.17.114.12:5671) has a client-provided name: rabbitConnectionFactory#0

2020-09-29 15:47:24.637 [info] <0.2478.160> connection <0.2478.160> (10.20.15.115:55750 -> 10.17.114.12:5671 - rabbitConnectionFactory#0): user 'john.doe' authenticated and granted access to vhost 'vhost001'

2020-09-29 15:47:45.313 [info] <0.2478.160> closing AMQP connection <0.2478.160> (10.20.15.115:55750 -> 10.17.114.12:5671 - rabbitConnectionFactory#0, vhost: 'vhost001', user: 'john.doe')