[Bobby Hata]

Is there a way to tell, maybe some kind of log file of when the Mac was used?

Thanks,
Bobby

[Captain Obvious]

I am going to assume you are asking this because you want to know when others are using your comp when you aren't around. Well, lets start off with the built in security function on any OS 9.x or OS X.
You can turn on the multiple users control panel and activate the Multiple user Accounts. This will require you to enter a password when you first boot the computer. There are a few apps and screen savers that do the same thing but this one is free.
Then there are a few programs that can record screen shots or key strokes. (like monitorer
This way when you log on you can see what others were up to while you were gone. Sneaky, yes but effective. Furthermore in some states not telling a person that this type of software is installed on YOUR computer is illegal. And using anything obtained as a result of the program (for let's say prosecution, divorce, etc.), will render the info inadmissible. Its considered along the same lines as wiretapping. Anyway that's just an FYI.....

If this isn't what you wanted to know then I recommend you expand on your post and detail what it is you want to know about your computer and what aspect of it being on you want to know.

[neutrino23]

Perhaps a developer can tell us about a log file. One simple idea is to boot up from a CD and then look at the preference files in the System Folder on the Hard Drive. Probably the Finder Preferences or something similar get updated when you shut down. Just look at the Preferences Folder in List View and sort by date modified.

[neutrino23]

One more idea. You could write something that would write the time and date to a log file when executed. Then put this in the "shutdown items" folder. One way to write this would be with Applescript.