Formula for db gain and logarithm makes no sense.

Well, I suppose I have to admit to being brain dead, here, but I can't seem to figure out how this formula produces the db results stated.



I'm studying the book "Live Sound Reinforcement" by Teddy Boyce, and I'm stuck on page 12 with the following example of how to find db.



He says:

input power is .2 W

output power is 800w



The formula for db is:

db = 10log (output power/input power)



Results:

Gain of amplifier

[top] 800/.02

4000 no surprises here.



But continuing results reveals:

Gain of amplifier in db

[top] 10log (800/.2)

10log (4000) again, no surprises so far

= 36 db but here, I don't understand how this formula yields 36 db.



It looks like everything is in multiples of ten, so how does he get 36 db out of all that?



Can someone with a brain please explain this to me?

Thanks so much.

Formula for db gain and logarithm makes no sense.