A log scale, formally known as a logarithmic scale, measures exponential values rather than unit values as a linear scale does. This is useful when values change more rapidly than is convenient to represent on a linear scale. Many physical phenomena are most easily measured with a logarithmic scale, making them very common in science and engineering. For example, our senses of sight and hearing function on a logarithmic scale such that doubling the actual intensity of the input increases its perceived intensity by a constant amount.

- Skill level:
- Moderate

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## Instructions

- 1
Define a logarithm. For the equation x = b^y, y is the logarithm of x to the base b. Therefore, if x = b^y, then y = logb(x). The most common base for a logarithmic scale is 10.

- 2
Determine values on a linear scale. The unit markings on a linear scale indicate integer values such that the first unit marking indicates 1, the second unit marking indicates 2, the third unit marking indicates 3 and so on.

- 3
Examine a logarithmic scale. The unit markings on a logarithmic scale indicate the values given by raising the logarithm's base to the power of each integer.

- 4
Read the unit values on a logarithmic scale. The first unit marking indicates 10^1 = 10, the second unit marking indicates 10^2 = 100, the third unit marking indicates 10^3 = 1,000 and so on.

- 5
Look at negative values on a logarithmic scale. On this scale, the unit marking of -1 indicates 10^-1 = 0.1, the unit marking of -2 indicates 10^-2 = 0.001, the unit marking of -3 indicates 10^-3 = 0.001 and so on. Note that negative numbers on a logarithmic scale indicate numbers between 0 and 1 instead of negative numbers.