Looking for a log file telling me when my phone was on? My android 4.4.3 phone was off and in storage but when I got it back the battery was flat and there was some stuff on facebook I can't account for. Is there any log files which would confirm when my phone was on etc.
I found this answer useful. It might help you with what you're looking to accomplish: 

Log file locations

As an alternative, there's an app that can help you analyze logs: 

aLogcat (free) - logcat