First, let me start by saying I know this is an older thread. I only comment so that others that find this while poking around the net (as I did today) will have a clear answer.
Second, please note that the following command is bad practice and falls under the "useless uses of cat" (google search for it) category...
cat /var/log/messages | grep "`LC_ALL=en_en.utf8 date +"%b %e"`"
That line should be changed to:
grep "`LC_ALL=en_en.utf8 date +"%b %e"`" /var/log/messages
grep, and most unix/linux commands (sed, awk, etc...) for that matter do not require cat to read a files contents. It is sufficient to place the file path and name after the command to pass it as an argument. Adding a pipe and another external command (cat) is just wasted time and resources.
Finally, As to where to find a record of system shutdowns and/or reboots, use the last command as that is exactly what it is meant for. It reads the /var/log/wtmp log file for all login/logout entries. Because shutdowns and reboots are actually a system level login/logout event, they are recorded here. The same applies for root console shutdown, it is a logout event.
last -5 reboot shutdown root
This will give you the last 5 reboot, shutdown, and root (console shutdown included) entries in the wtmp log.
reboot ~ Mon Mar 23 14:51
shutdown ~ Mon Mar 23 14:49
root console Mon Mar 23 14:49 - shutdown (00:00)
reboot ~ Mon Mar 16 09:54
shutdown ~ Thu Mar 12 17:41
I hope this helps anyone that stumbles across this thread. :-)