Particular Bases
Among all choices for the base b, three are particularly common. These are b = 10, b = e (the irrational mathematical constant ≈ 2.71828), and b = 2. In mathematical analysis, the logarithm to base e is widespread because of its particular analytical properties explained below. On the other hand, base-10 logarithms are easy to use for manual calculations in the decimal number system:
Thus, log10(x) is related to the number of decimal digits of a positive integer x: the number of digits is the smallest integer strictly bigger than log10(x). For example, log10(1430) is approximately 3.15. The next integer is 4, which is the number of digits of 1430. The logarithm to base two is used in computer science, where the binary system is ubiquitous.
The following table lists common notations for logarithms to these bases and the fields where they are used. Many disciplines write log(x) instead of logb(x), when the intended base can be determined from the context. The notation blog(x) also occurs. The "ISO notation" column lists designations suggested by the International Organization for Standardization (ISO 31-11).
| Base b | Name for logb(x) | ISO notation | Other notations | Used in |
|---|---|---|---|---|
| 2 | binary logarithm | lb(x) | ld(x), log(x), lg(x) | computer science, information theory, mathematics |
| e | natural logarithm | ln(x) | log(x) (in mathematics and many programming languages) |
mathematical analysis, physics, chemistry, statistics, economics, and some engineering fields |
| 10 | common logarithm | lg(x) | log(x) (in engineering, biology, astronomy), |
various engineering fields (see decibel and see below), logarithm tables, handheld calculators |
Read more about this topic: Logarithm
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