Why Power ratios in decibels use dB = 10 x log10(P2/P1). For a ratio of 2, log10(2) = 0.301, so the change is 10 x 0.301 = about 3 dB (positive for doubling, negative for halving). This is why 3 dB is called the half-power point on filter and antenna response curves.
Watch out The choice near 6 dB is the value you get for doubling voltage or current (20 x log10(2)), or for quadrupling power, not for doubling power.
Double the power = 3 dB. Double the voltage = 6 dB. Ten times power = 10 dB.
The digit 3 is two bumps stacked up: 3 dB doubles the power. Six is two 3s, and that one is for voltage.