The logs that Avast 2016 in regards to actions it takes on files such as deleting, quarantining, cleaning & etc make are stored in the following directory:
%programdata%\avast software\avast\report
Logs that pertain to the operation of the Avast software such as updates can be found here:
%programdata%\avast software\avast\log
You can access either of these folders easily by using Windows Key + R and copy and pasting one of the paths from above and clicking OK
or pressing the Enter/Return key.