*Kiddle Encyclopedia.*

# Logarithmic scale facts for kids

Various scales: lin-lin, lin-log, log-lin and log-log. Plotted graphs are: y=x (green), y=10^{x}(red), y=log(x) (blue). |

A **logarithmic scale** is a scale of measurement that uses the logarithm of a physical quantity instead of the quantity itself. On a logarithmic scale, each tick mark on the scale is the previous tick mark *multiplied* by some number.

The logarithmic scale can be helpful when the data covers a large range of values – the logarithm reduces this to a more manageable range.

Some of our senses operate in a logarithmic fashion (multiplying the actual input strength adds a constant to the perceived signal strength, see: Stevens' power law). That makes logarithmic scales for these input quantities especially appropriate. In particular, our sense of hearing perceives equal *multiples* of frequencies as equal *differences* in pitch.

On most logarithmic scales, *small* multiples (or ratios) of the underlying quantity correspond to *small* (possibly negative) values of the logarithmic measure.

## Examples

Well-known examples of such scales are:

- Richter magnitude scale and Moment magnitude scale (MMS) for strength of earthquakes and movement in the earth.
- bel and decibel and neper for acoustic power (loudness) and electric power;
- cent, minor second, major second, and octave for the relative pitch of notes in music;
- logit for odds in statistics;
- Palermo Technical Impact Hazard Scale;
- Logarithmic timeline;
- counting f-stops for ratios of photographic exposure;
- rating low probabilities by the number of 'nines' in the decimal expansion of the probability of their not happening: for example, a system which will fail with a probability of 10
^{−5}is 99.999% reliable: "five nines". - Entropy in thermodynamics.
- Information in information theory.
- Particle Size Distribution curves of soil

Some logarithmic scales were designed such that *large* values (or ratios) of the underlying quantity correspond to *small* values of the logarithmic measure. Examples of such scales are:

- pH for acidity;
- stellar magnitude scale for brightness of stars;
- Krumbein scale for particle size in geology.
- Kardashev scale for technological advance in physics.
- Absorbance of light by transparent samples.

## Graphic representation

A logarithmic scale is also a graphical scale on one or both sides of a graph where a number *x* is printed at a distance *c*·log(*x*) from the point marked with the number 1. A slide rule has logarithmic scales, and nomograms often employ logarithmic scales. On a logarithmic scale an equal difference in order of magnitude is represented by an equal distance. The geometric mean of two numbers is midway between the numbers.

**Logarithmic graph paper**, before the advent of computer graphics, was a basic scientific tool. Plots on paper with one log scale can show up exponential laws, and on log-log paper power laws, as straight lines (see semilog graph, log-log graph).