Which decibel value most closely represents a power decrease from 12 watts to 3 watts?
Why Decibels compare powers as a ratio, not a difference. Going from 12 W to 3 W is a ratio of 1/4, and each halving of power is -3 dB, so two halvings give -3 dB + -3 dB = -6 dB. Formally, 10 log(3/12) = 10 log(0.25) = -6 dB.
Watch out The choice of -3 dB would be right only if the power dropped by half, to 6 watts; subtracting 12 - 3 = 9 and reading it as -9 dB confuses a difference with a ratio.
Half = 3 dB, quarter = 6 dB, tenth = 10 dB. Count doublings or halvings, not watts subtracted.