A scale describes the relationship between two quantities. The logarithmic scale differs from a linear scale in that the proportion between two quantities isn't constant but rather, has a logarithmic rate. The following table highlights the different proportions, one linear and the other logarithmic, between two quantities X and Y:
Table 3.1. Comparison of a linear scale with a logarithmic scale

The Bel is defined as the logarythm of the ratio between a quantity and its reference value. 1 Decibel equals 10Bel, so the decibel relating to a quantity X is expressed as follows:
Equation 3.1. dB_{X}
Which states decibel variations of the quantity X in relation to a fixed reference value X_{0}.
If for example, the quantity we're considering is X and our reference value is X_{0} = 10, going from X_{0} to X=1000, we obtain an increase in dB expressed in the following formula: