Why is voltage gain in dB given by 20 Log but power gain by 10 Log?

[likephysics]

Why is voltage gain in db given by

20 Log (v2/v1)

but power gain is straight forward : 10 Log (p2/p1).

 

[Bob S]

Remember that Log(x²) = 2·Log(x)

Bob S

 

[skeptic2]

The gain in dB is power gain. When you are expressing the voltage gain, the gain must be squared in order to convert it to power gain so that when gains are compared they in fact are comparable. (This assumes the voltages are across the same impedance.) Squaring the voltages is the same as adding a factor of 2 ahead of the Log as Bob S shows above.