A logarithm is a mathematical operation, the result of which is an exponential power of the base.
base 10 logarithm = log10 = common logarithm = log
log10 10ⁿ = log 10ⁿ = n
101 = 10 log 10 = 1
100 = 1 log 1 = 0
log xy = log x + log y
log x/y = log x - log y
log xⁿ = n log x
101 = 10 log 10 = 1 log 10ⁿ = n log 10 = n
Decibels dB expresses the ratio of two values as a common logarithm times 10
dB has no units, equal units in the numerator and denominator of the ratio cancel
dB = 10 log (value 2 / value 1)
dB = 10 log (power 2 / power 1)
Power P = V² / Z
dB = 10 log (voltage² 2 / voltage² 1) = 20 log (voltage 2 / voltage 1)
If value 1 is a reference value, the units may be stated
The reference level is 0 dB = 10 log 1 value 2 = value 1 value 2 / value 1 = 1
Sound level is not linear, sound level is exponential
Sound level is measured in dB Sound Pressure Level
dB Sound Intensity Level = dB Sound Pressure Level
Reference Sound Intensity value = 1 picowatt per meter² = 10-12 Watt per meter²
Reference Sound Pressure value = 20 micropascals µPa
Sound Intensity = Sound Power / surface area
Surface area of a sphere = 4 π r² r = radius = distance
dB Sound Intensity Level = 10 log (Sound Intensity 2 / Sound Intensity 1)
10 log (Sound Intensity 2 / Sound Intensity 1) = 10 log (distance² 1 / distance² 2)
10 log (distance² 1 / distance² 2) = -20 log (distance 2 / distance 1)
dB Sound Intensity Level = dB Sound Pressure Level
base 2 logarithm = log2
log2 2ⁿ = n
log10 2ⁿ = n log10 2 log10 2ⁿ / log10 2 = n
octaves = log2 (frequency 2 / frequency 1)
12 semitones = 1 octave equal temperament
base x logarithm = logx
logx xⁿ = n
x1 = x logx x = 1
x0 = 1 logx 1 = 0
logx yz = logx y + logx z
logx y/z = logx y - logx z
logx yⁿ = n logx y logx yⁿ / logx y = n
x1 = x logx x = 1 logx xⁿ = n logx x = n
Audiophile Heretic, July 4, 2026 Menu