Is there a log that records shutdowns in Linux?

Problem

I was wondering if there is a log file in Linux which records every time the computer is shut down? The reason I am asking is I am doing some tests involving how long my laptop battery lasts under certain conditions. My laptop is configured to automatically shut down when there is about 10 minutes of battery power left, so if there is a log file somewhere that records when the computer is shut down, this will make my testing much easier. I'm running Ubuntu 10.04. Thanks!