Yes, the Bel, and therefore the deciBel (dB) are defined as power ratios.
As a calculation aid, assuming that the impedance at both measurements is the same, the factor of 20 can be used to calculate that ratio in dB, since P = V^2/R and log(V^2) = 2 log (V).
Where this gets really tricky to keep track is in optoelectronics, where the output current of a photosensor is proportional to the optical power incident on the sensor. Therefore, if you attenuate the optical power by 3 dB, you must increase the gain of the amplifier after the sensor by 6 dB to get the same output.