How to log commands executed by all the users in Linux?

By adding the following entry in /etc/bashrc, we can log the commands executed by all the users on a Linux machine. 
This would be certainly helpful for tracking commands on Critical servers.

PROMPT_COMMAND='history -a >(logger -t "$USER[$PWD] $SSH_CONNECTION")'

After you add the above entry at the end of /etc/bashrc file, execute the command 'source /etc/bashrc' or logout and login back to your session. Now the commands executed by all the users will be logged in /var/log/messages.

Note: If you wish to log the commands on to a different file, please check the solution given in the comments section.

Sample test result:

Apr 18 13:35:21 Linux-Mach root[/root] 192.168.4.5 51650 172.16.0.252 22: uptime
Apr 18 13:35:24 Linux-Mach root[/opt] 192.168.4.5 51650 172.16.0.252 22: cd /opt
Apr 18 13:35:26 Linux-Mach root[/opt] 192.168.4.5 51650 172.16.0.252 22: ls -lR
Apr 18 13:35:35 Linux-Mach root[/opt] 192.168.4.5 51650 172.16.0.252 22: iostat -x 2
Apr 18 13:35:39 Linux-Mach root[/root] 192.168.4.5 51650 172.16.0.252 22: cd /root
Apr 18 13:35:39 Linux-Mach root[/root] 192.168.4.5 51650 172.16.0.252 22: ls -l
Apr 18 13:35:51 Linux-Mach root[/home] 192.168.4.5 51650 172.16.0.252 22: cd /home
Apr 18 13:35:52 Linux-Mach root[/home] 192.168.4.5 51650 172.16.0.252 22: ls
Apr 18 13:35:56 Linux-Mach root[/home] 192.168.4.5 51650 172.16.0.252 22: httpd -t

Apr 18 13:51:24 Linux-Mach test1[/home/test1] 192.168.6.8 9106 172.16.0.252 22: ls -l
Apr 18 13:53:20 Linux-Mach test1[/var/lock/subsys] 192.168.6.8 9106 172.16.0.252 22: cd /var/lock/subsys
Apr 18 13:53:30 Linux-Mach test1[/var/lock/subsys] 192.168.6.8 9106 10.160.0.252 22: ls -ltr

Updated one:

# echo $PROMPT_COMMAND

RETRN_VAL=$?;logger -p local3.debug "$(whoami)  $remoteip  [$$]: $(history 1 | sed "s/^[ ]*[0-9]\+[ ]*//") [$RETRN_VAL]"

On RHEL 8.x

[root@rhel8 ]# cat /etc/profile.d/prompt.sh 

remoteip=$(who am i | awk '{print $5}' | sed "s/[()]//g")

export PROMPT_COMMAND='RETRN_VAL=$?;logger -p local3.debug "$(whoami)  $remoteip  [$$]: $(history 1 | sed "s/^[ ]*[0-9]\+[ ]*//") [$RETRN_VAL]"'

[root@rhel8 ]#