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Logarithmic Expressions

Mathematical Composition

Stephen J. Lurie

Logarithmic Expressions

The term log is an abbreviation of logarithm. A system of logarithms may be based on any number, although logarithmic systems based on the numbers 10, 2, and the irrational number e are most common. The base should be subscripted and follow the word log. In the following examples, note that logarithms are always computed from exponents of the number that forms their basis.

log10 1000 = 3 (because 1000 = 103)

log2 8 = 3 (because 8 = 23)

Logarithms based on e (which is approximately 2.71) are called natural logarithms and are often represented as ln.

ln 2.71 = 1

The terms “ex” and “exp x” are identical in meaning and are interchangeable. The latter is preferable for constructions involving additional subscripts or superscripts. For instance, “exp (x3 − 1)” is identical to ex31, but the former is preferred because it is easier to set and to read.

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