Can anyone teach me the basics of this engineering maths question step by step to a complete math novice?

Question

PLEASE HELP ME WITH QUESTION B, I just dont understand logs law or anything to do with it:)
Can anyone actually explain to me how this mathematics question was does as I had it in an engineering test but couldn't do it:
The power gain of an amplifier relates input power, Pi, to output power, Po, by;
Power gain= 10log(small 10) Po/Pi decibles (dB)
a) As part of the assesment of a new system you have been asked to find the power gain when Po=15W and Pi=300mW
B) you also have to find out what the output power will be if input power is 400mW and the power gain is 20dB.


Please may someone explain this to me step by step as it completely mindblows me, thanks to anyone who can help me it will be much appreciated.

Thanks everyone :)

Answer 1

WOW, you again??? I answered this question like 10 times for you. You don't even have to know anything about logs on part A. You just need to punch the numbers of the equation into a calculator! Part B you man need to know a little about logs, but not much.

Here it is again:


For Part A)
First of all i'm assuming that when you say small 10 you mean base 10.

Just substitute Po and Pi in the equation:

power gain = 10*log(15/.3) = 19.99 dB

B)
Since you know the power gain and Pi you can solve for Po:

20 = 10*log(Po/.4)

divide both sides by 10
2 = log(Po/.4)

Since the log is base 10, when you raise both sides of the equation by the base 10 it cancels the log.

10^(log Po//4) = Po/.4
Therefore when you raise each to the base of 10 you get:

10^2 = Po/.4

Then Multiply both sides by .4
Po = 100*.4 = 40

Therefore adding the units of Watts you get:
Po = 40W

Answer 2

a) substitute Po and Pi in the equation:
power gain = 10 log(15/.3) = 19.99 dB

b) solve for Po:

20 = 10log(Po/0.4)
2 = log(Po/0.4)

10^(log Po//4) = Po/0.4
10^2 = Po/0.4
Po = 100(0.4) = 40

Therefore adding the units of Watts you get:
Po = 40W