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For example, the process of rewriting a fraction into one with the smallest whole-number denominator possible (while keeping the numerator a whole number) is called "reducing a fraction". Rewriting a radical (or "root") expression with the smallest possible whole number under the radical symbol is called "reducing a radical". Minimizing the ...
In mathematics, the logarithm to base b is the inverse function of exponentiation with base b. That means that the logarithm of a number x to the base b is the exponent to which b must be raised to produce x. For example, since 1000 = 10 3, the logarithm base of 1000 is 3, or log 10 (1000) = 3.
The identities of logarithms can be used to approximate large numbers. Note that log b (a) + log b (c) = log b (ac), where a, b, and c are arbitrary constants. Suppose that one wants to approximate the 44th Mersenne prime, 2 32,582,657 −1. To get the base-10 logarithm, we would multiply 32,582,657 by log 10 (2), getting 9,808,357.09543 ...
A term rewriting given by a set of rules can be viewed as an abstract rewriting system as defined above, with terms as its objects and as its rewrite relation. For example, x ∗ ( y ∗ z ) → ( x ∗ y ) ∗ z {\displaystyle x*(y*z)\rightarrow (x*y)*z} is a rewrite rule, commonly used to establish a normal form with respect to the ...
In computer science, lg * is often used to indicate the binary iterated logarithm, which iterates the binary logarithm (with base ) instead of the natural logarithm (with base e). Mathematically, the iterated logarithm is well defined for any base greater than e 1 / e ≈ 1.444667 {\displaystyle e^{1/e}\approx 1.444667} , not only for base 2 ...
Many of the following antiderivatives have a term of the form ln |ax + b|.Because this is undefined when x = −b / a, the most general form of the antiderivative replaces the constant of integration with a locally constant function. [1]
The logarithm in the table, however, is of that sine value divided by 10,000,000. [1]: p. 19 The logarithm is again presented as an integer with an implied denominator of 10,000,000. The table consists of 45 pairs of facing pages. Each pair is labeled at the top with an angle, from 0 to 44 degrees, and at the bottom from 90 to 45 degrees.
A similar problem, involving equating like terms rather than coefficients of like terms, arises if we wish to de-nest the nested radicals + to obtain an equivalent expression not involving a square root of an expression itself involving a square root, we can postulate the existence of rational parameters d, e such that
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