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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.
Logarithms can be used to make calculations easier. For example, two numbers can be multiplied just by using a logarithm table and adding. These are often known as logarithmic properties, which are documented in the table below. [2] The first three operations below assume that x = b c and/or y = b d, so that log b (x) = c and log b (y) = d.
The basic idea of the algorithm is due to Western and Miller (1968), [4] which ultimately relies on ideas from Kraitchik (1922). [5] The first practical implementations followed the 1976 introduction of the Diffie-Hellman cryptosystem which relies on the discrete logarithm. Merkle's Stanford University dissertation (1979) was credited by Pohlig ...
This definition gives rise to a function that coincides with the binary logarithm on the powers of two, [3] but it is different for other integers, giving the 2-adic order rather than the logarithm. [4] The modern form of a binary logarithm, applying to any number (not just powers of two) was considered explicitly by Leonhard Euler in 1739 ...
The sum of probabilities + is a bit more involved to compute in logarithmic space, requiring the computation of one exponent and one logarithm. However, in many applications a multiplication of probabilities (giving the probability of all independent events occurring) is used more often than their addition (giving the probability of at least ...
It states that under appropriate conditions the logarithm of a summation is essentially equal to the logarithm of the maximum term in the summation. These conditions are (see also proof below) that (1) the number of terms in the sum is large and (2) the terms themselves scale exponentially with this number.
In mathematics, the polylogarithm (also known as Jonquière's function, for Alfred Jonquière) is a special function Li s (z) of order s and argument z.Only for special values of s does the polylogarithm reduce to an elementary function such as the natural logarithm or a rational function.
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 ...