Logarithmic scale

Logarithmic scale

A Logarithmic scale is a nonlinear scale used when there is a large range of quantities. Common uses include earthquake strength, sound loudness, light intensity, and pH of solutions.

Overview[edit]

In a logarithmic scale, each tick mark on the scale is the previous tick mark multiplied by a value. Logarithmic scales are also used in slide rules for multiplying or dividing numbers by adding or subtracting lengths on the scales.

The decibel and the pH scale are logarithmic scales. What these scales have in common is that each step of equal distance from the last is a multiplication by the same factor, for example 10.

Mathematical basis[edit]

The logarithm to base b of a number x is the inverse function of b to the power x. In other words, if y = logb(x), then x = by. In the equation y = logb(x), the base b could be any positive number except 1, although often the base is 10, especially in scientific usage, or the base is the transcendental number e, especially in mathematical and some scientific usage.

Applications[edit]

Logarithmic scales are used in many areas of science and engineering:

Decibels measure sound intensity
pH measures the acidity or alkalinity of a solution
Richter scale and moment magnitude scale measure earthquakes
Logarithms are used in computing to reduce multiplication operations to addition and division to subtraction.