Preliminary remarks

Base 10 logarithms, often called common logarithms, appear in many scientific and applied formulas.

For example, earthquake intensity is often reported on the logarithmic Richter scale. Here the formula is

where a is the amplitude of the ground motion in microns at the receiving station, T is the period of the seismic wave in seconds, and B is an empirical factor that allows for the weakening of the seismic wave with increasing distance from the epicenter of the earthquake. For an earthquake 10,000 km from the receiving station, B = 6.8. Thus if the recorded vertical ground motion is a = 10 microns and the period is T = 1 sec, the earthquake's magnitude, following (6), is R = 7.8. An earthquake of this magnitude does great damage near its epicenter.

Another example of the use of common logarithms is the decibel scale using, particularly, for measuring loudness. (The decibel unit is named in honor of Alexander G. Bell (1847-1922), inventor of the telephone.) If I is the intensity of sound in watts per square meter, the decibel level of the sound is

where I₀ is an intensity of 10^-12 watts per square meter corresponding roughly to the faintest sound that can be heard.