﻿ ﻿Exponents - Mathematical Composition

# ExponentsMathematical Composition

Use of radicals (eg, any expression that contains a radical symbol: √) may sometimes be avoided by substituting a fractional exponent: As with unstacking fractions, if clarity is sacrificed by making the equation fit within the text, it is preferable to set it off. For example, E = 1.96{[P(1 − P)]/m}1/2 may fit within the text, but the equation set off and centered as below might be more easily understood: 20.3.2 Negative Exponents.

A negative exponent denotes the reciprocal of the expression, as illustrated in these examples:  20.3.3 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.  Logarithms based on e are called natural logarithms and are often represented as ln. The terms “ex” and “exp x” are identical in meaning and are interchangeable. The latter is preferable for constructions that involve additional subscripts or superscripts. For instance, exp (x3 − 1) is identical to ex3−1, but the former is preferred because it is easier to read and typeset.

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