My apologies, originally when I saw your post I assumed it related to actual server related files, however now I realise you may have been referring to transaction logging in terms of Paypal payments?
If you're referring to logging of Paypal transactions, then yes, the Ultimate edition licence includes this
feature (indicated under "payment gateways" section).
Click here to view a screenshot
If this is not what you meant, and you were referring to database log files, then please let us know.