Linux: Why does the last command output incorrect data?

Question

linux

I periodically look when the computer was turned off with this command: last -x3 shutdown
After reinstalling the system (Ubuntu 15.10), the command began to display incorrect data.
For example, now it shows that the computer was turned off 3 days ago - even though I turn it off at night every day. Yes, and the time that is displayed is not true:

shutdown system down  4.2.5-040205-gen Fri Nov  6 15:46 - 18:46  (03:00)

Probably, last has nothing to do with it - this command simply displays what they "give", and the problem is in logging. I installed the system with minimal cd, maybe I didn't install any packages?