Update: if you become root via sudo, then do last, it will pause a few seconds and then spew out the answers. I believe after that point it will also work for non-root users.
Open /Applications/Utilities/Console app and look at logs to see if you see it there. Then if you want to rerun your log cleaning jobs then down an application like Yasu or Onyx and run all the "cleaning routines and let the program reboot your Mac. Then after that boot immediately reboot again to completely rebuild your system's startup/shutdown cache.
The unix way of running those "cron" jobs is running the Terminal command: