The majority of the output from OpenVZ is going to be written to /var/log/messages and the action output for vzctl is going to be written to /var/log/vzctl.log.
The vzctl.log file is the logfile were vzctl stores the output for its actions. The logfile is rotated monthly for historical reference.
If you run the ls /var/log/vzctl.* command, you will get the following output:
ls /var/log/vzctl.* /var/log/vzctl.log /var/log/vzctl.log-20120221
Here is a sample output of the current logfile:
less /var/log/vzctl.log
In the previous example, you can see the output from the last time we used the vzctl command to make changes to the CPU limits of container 101. If you need to go and reference the changes that have been made using vzctl, use this log.