dmesg is a standard Unix terminal command that displays the contents of one of the main system log files. It requires superuser access, so use "sudo" before it to give yourself that access. Open a terminal, type "sudo dmesg" and then enter, and type in your password when you are asked to do so.
But I'm afraid there isn't much in that log of use to you. All that will tell you is whether an Apple tech powered up the computer and booted from that drive (and you'd have to figure that out from the timestamps). If they boot from a different drive, nothing will be added to the logs on your drive. And there is no way to tell if an Apple tech has simply opened the case.
If you compare the logs before and after you power up, you might be able to find out that certain components may have changed using unique identifiers, like MAC addresses or serial numbers. But paging through the log files can be confusing if you don't know what to look for. Instead, run System Profiler, and save the results before you send the Mac out for repair, then run it afterwards, open the old file, and manually compare the two windows.
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