In many natural phenomena quantities vary over radically different orders of magnitude: the intensity of a sound can range from 101210^{-12} to 1010 watts per square metre, the energy of earthquakes from 10010^0 to 101810^{18} joules, the concentration of H+^+ ions from 101410^{-14} to 10010^0 mol/L. Representing such different values on a linear scale is impossible: one then uses a logarithmic scale, in which the distance between two values is not their difference but the logarithm of their ratio. This section applies the logarithm to real scales: the logarithmic scale itself, decibels and other notable scales (Richter, pH, stellar magnitudes).