I was just pointing out your error in confusing power and loudness.
There seems to be further errors in this post though.
If your gunshot is 160dB and your bat 70 - 100dB then the loudness difference is actually between 64 and 512 times louder not between 128 and 512 times louder.
I don't think that 70dB is anywhere near loud enough for the bat. He would not have been tapping the door he was trying to break it. 70dB is a vacuum cleaner. Clearly hitting a door could be heard over this. 90dB, the noise close to a busy road would be much more like it.
BTW if you take the gunshot is 160dB and put the bat at just 80dB then the power difference is nothing like 1000x. It is actually 10^8 which is 100,000,000x
Hang on.....what?
We are talking about sound! Acoustics!
A decibel is just a unit of measurement. It's used in lots of different ways, in lots of different disciplines to stop the numbers being worked with getting too huge.
It's amplitude we're interested in here. How much the sound waves produced have displaced the normal atmospheric pressure. We can then measure that in relation to the smallest sound detectable to the human ear to find the sound pressure level. Here a gain of 20db is x10.
I'm sure that there is a relationship between power, voltage and bat sounds, but it's far beyond the expertise of me and you, that's for sure. And how does it help on this thread?
A gain of 60db gives a sound 1000 times louder. Yes....LOUDER. The sound is that much louder.
If we then want to work out how this translates to individual ears...the perception...then we need access to information neither of us have.
A gun shot is MASSIVELY louder than any bat sound. That's it.
Regarding my calculation - I worked out the difference between 70db and 160db as 512 times louder...I mean...more intense.
Then I got distracted, decided in the interests of simplicity to give you 90db (which I agree is more realistic than 70db) and didn't bother recalculating.
So, I accept your correction there. I was being lazy.
IMPORTANT EDIT: I missed out an important part of my explanation. Attenuation. The SPL is run through an electronic meter that mimics the way human ears hear high and low frequencies and this gives a numerical value of 1000. The actual db is called db(A) SPL and this is what's referenced with all those tables that show db levels for vacuum cleaners and jet engines. A bald statement saying 20db = x10 does not give a true reflection of what we hear because we don't hear sounds in the flat way that that suggests.
And since I am both boring and confusing myself now, I shall leave it there.
A bat sound is 1000 times (roughly) quieter than a gun shot. I'll stand firm on that.