Decibels aren't too hard, but don't get too caught up in needing to know too many values. Really if you need a specific value its easiest to just use a calculator. If you just need a ballpark, it's not too hard. It's just a way of representing larger numbers using smaller numbers.
The formula for comparing two power level is 10log(P1/P0). A quantity express in DB is a ratio. It is the level of a signal compared to something else. A common one is dBm, or dB milliwatt, the value of a power signal compared to a milliwatt (at least in RF its commonly used). As you've seen, the dB values for raios of 10, 100, 1000 are pretty easy (10dB, 20dB, 30dB). Anything off of those values are a little harder.
the only other trick to remembering values is to remember that each time a power signal level doubles, it goes up by 3dB. If it doubles again, it goes up by another 3dB. If a power signal decreases by half, it goes down by 3dB.
The table shows a power level, starting at 1mW. The column on the right shows the DB level of the signal compared to the original signal (1mW). Notice that each time the power level doubles, the signal increases by 3dB. I've also included the 10, 100, 1000 so you can see where they fit in.
Power
Level dBlevel
1mw 0
2 3
4 6
8 9
10 10
16 12
32 15
64 18
100 20
128 21
256 24
512 27
1000 30
1024 30(using the doubles each time method)
2048 33
4096 36
8192 39
10000 40
16384 42
It really doesn't matter where you start. if you have a 40Watt signal, if it goes up to 80Watts, it has increased by 3DB.
If you are talking about comparing voltage levels, its a little different. The formula uses a 20log(v1/v0) instead of the 10log. It boils down to a voltage level increases 6dB each time the actual level doubles, or decreases 6dB if its level is halved. Again, most of the time dB are used to refer to power levels.
