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Basic Mathematics - Log Scales

A logarithm is an exponent (power) to which a base number must be raised to yield the same result. The standard logarithm scale is called base 10. The term "log" is used when specifying a log scale.

In base 10, the log of 100 = 2:

When basing your equation on base 10, indicating the base is not required as base 10 is implied:

Other bases can be used, such as base 2, or base 3, or even base 25:

The reason for using a log scale is so we can evaluate our data easier. For example, a chart of data can either look like a boring straight line, or with a log system applied, a more dynamic chart is created:

The graph above is nothing in particular, but the blue line will be raw data, and the pink line will be the same data using a base 10 log scale.

A perfect example of logarithm used in Astronomy is the Hertzsprung-Russell diagram, a diagram of stars.

This diagram is an example of a Hertzsprung-Russell Diagram (H-R diagram). Astronomers already have the data in log form, so an example of an H-R diagram with just raw data only is hard to find, but the dots will reside in the lower half of the graph and the curves will not be apparent.

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