A few examples of how logarithms are used in the real world include measuring the magnitude of earthquakes or the intensity of sound and determining acidity. A logarithm explains how many times a number is multiplied to a power to reach another number. It is expressed as loge(x) and is commonly written as ln(x).
A logarithm used to describe the intensity of an earthquake can be expressed as R = log I. "R" is equal to the magnitude of the earthquake, which is measured by the Richter scale. "I" is equal to the intensity of the earthquake when measured against the reference value. The reference value is equal to lo = 1 and is the smallest level at which seismic activity can be detected. An increase of 1 on the Richter scale means the magnitude of the earthquake is 10 times greater.
Sound intensity can be expressed as β = 10 log ( I / I0 ). Sound is measured in decibels, and I0 is the smallest intensity that can be heard by the human ear. An increase in 10 decibels is equal to an increase in sound that is 10 times the intensity. Acidity can be expressed as pH = - log [H+]. The pH of a substance measures how acidic or basic it is.