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The graph of the logarithm base 2 crosses the x-axis at x = 1 and passes through the points (2, 1), (4, 2), and (8, 3), depicting, e.g., log 2 (8) = 3 and 2 3 = 8. The graph gets arbitrarily close to the y-axis, but does not meet it. Addition, multiplication, and exponentiation are three of the most fundamental arithmetic operations.
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 = 9,808,357 + 0.09543. We can then get 10 9,808,357 × 10 0.09543 ≈ 1.25 × 10 9,808,357. Similarly, factorials can be approximated by summing the logarithms of the ...
Historically', the "common logarithm" was known by its Latin name logarithmus decimalis [2] or logarithmus decadis. [ 3 ] The mathematical notation for using the common logarithm is log( x ) , [ 4 ] log 10 ( x ) , [ 5 ] or sometimes Log( x ) with a capital L ; [ a ] on calculators , it is printed as "log", but mathematicians usually mean ...
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[2] A familiar example of logarithmic growth is a number, N , in positional notation , which grows as log b ( N ), where b is the base of the number system used, e.g. 10 for decimal arithmetic. [ 3 ]
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In mathematics, for given real numbers a and b, the logarithm log b a is a number x such that b x = a.Analogously, in any group G, powers b k can be defined for all integers k, and the discrete logarithm log b a is an integer k such that b k = a.