Set the group of the file that needs to be executed to the group used by the three users, and chmod the file to... 770.

example:
-wrxwrx--- root jgroup /usr/bin/tail

in /etc/group (your milage may vary)
be sure john, brad and dave are in group jgroup.
Change as needed.

`ps` will show which user has executed the file, but only root and those in the group will be able to use the file.

Cheers,
-Seg

ps: to log who used it create a script file to echo $user $tty `date` to a file then execute the process...