The logs should reflect activity as it find it and as long as computer is running ok all should be well. If activity is found software logs it to whatever category it was and that helps to identify problems that could have resulted in your computer if you didn't have any protection in the first place.
It looks like you may have chosen to run your scans manually instead of having the scheduled scan do it automatically. I beleive the default setting is to run at 4am on Friday mornings. You can also schedule to run whenever you want it to run. If you turned your scheduled scan off this may explain why you have the gap in time. If your home screen shows green and MVT shows no errors then you should not have to worry about anything.