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

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

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

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.

See also

• Exponential growth
• Semi-log plot
• Logarithmic mean
• Bode plot
• Level (logarithmic quantity)
• Logarithmic timeline
• Logarithmic video amplification

Logarithmic scale

• Internet host count from 1988 to 2012 on a logarithmic scale
  Internet host count from 1988 to 2012 on a logarithmic scale
• Illustration of a logarithmic scale
  Illustration of a logarithmic scale
• Example of a slide rule
  Example of a slide rule
• Tsunami deaths data
  Tsunami deaths data
• Solar map
  Solar map
• Logarithmic scales
  Logarithmic scales
• Decreasing renewable energy costs versus deployment in 2010
  Decreasing renewable energy costs versus deployment in 2010