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For example, ln 7.5 is 2.0149..., because e 2.0149... = 7.5. The natural logarithm of e itself, ln e, is 1, because e 1 = e, while the natural logarithm of 1 is 0, since e 0 = 1. The natural logarithm can be defined for any positive real number a as the area under the curve y = 1/x from 1 to a [4] (with the area being negative when 0 < a < 1 ...
ln(r) is the standard natural logarithm of the real number r. Arg(z) is the principal value of the arg function; its value is restricted to (−π, π]. It can be computed using Arg(x + iy) = atan2(y, x). Log(z) is the principal value of the complex logarithm function and has imaginary part in the range (−π, π].
Calculators generally perform operations with the same precedence from left to right, [1] but some programming languages and calculators adopt different conventions. For example, multiplication is granted a higher precedence than addition, and it has been this way since the introduction of modern algebraic notation .
The logarithm keys (LOG for base 10 and LN for base e) on a TI-83 Plus graphing calculator Logarithms are easy to compute in some cases, such as log 10 (1000) = 3 . In general, logarithms can be calculated using power series or the arithmetic–geometric mean , or be retrieved from a precalculated logarithm table that provides a fixed precision.
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The calculation of the Meissel–Mertens constant. [30] Lower bounds to specific prime gaps. [31] An approximation of the average number of divisors of all numbers from 1 to a given n. [32] The Lenstra–Pomerance–Wagstaff conjecture on the frequency of Mersenne primes. [33] An estimation of the efficiency of the euclidean algorithm. [34]
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