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  2. Logarithm - Wikipedia

    en.wikipedia.org/wiki/Logarithm

    Because log(x) is the sum of the terms of the form log(1 + 2 −k) corresponding to those k for which the factor 1 + 2 −k was included in the product P, log(x) may be computed by simple addition, using a table of log(1 + 2 −k) for all k. Any base may be used for the logarithm table.

  3. Natural logarithm - Wikipedia

    en.wikipedia.org/wiki/Natural_logarithm

    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). The simplicity of this definition, which is matched in many ...

  4. Prime number theorem - Wikipedia

    en.wikipedia.org/wiki/Prime_number_theorem

    The first such distribution found is π(N) ~ ⁠ N / log(N) ⁠, where π(N) is the prime-counting function (the number of primes less than or equal to N) and log(N) is the natural logarithm of N. This means that for large enough N, the probability that a random integer not greater than N is prime is very close to 1 / log(N).

  5. Common logarithm - Wikipedia

    en.wikipedia.org/wiki/Common_logarithm

    A graph of the common logarithm of numbers from 0.1 to 100 In mathematics , the common logarithm is the logarithm with base 10. [ 1 ] It is also known as the decadic logarithm and as the decimal logarithm , named after its base, or Briggsian logarithm , after Henry Briggs , an English mathematician who pioneered its use, as well as standard ...

  6. List of logarithmic identities - Wikipedia

    en.wikipedia.org/wiki/List_of_logarithmic_identities

    The multiple valued version of log(z) is a set, but it is easier to write it without braces and using it in formulas follows obvious rules. log(z) is the set of complex numbers v which satisfy e v = z; arg(z) is the set of possible values of the arg function applied to z. When k is any integer:

  7. e (mathematical constant) - Wikipedia

    en.wikipedia.org/wiki/E_(mathematical_constant)

    The number e is a mathematical constant approximately equal to 2.71828 that is the base of the natural logarithm and exponential function.It is sometimes called Euler's number, after the Swiss mathematician Leonhard Euler, though this can invite confusion with Euler numbers, or with Euler's constant, a different constant typically denoted .

  8. Euler's constant - Wikipedia

    en.wikipedia.org/wiki/Euler's_constant

    The area of the blue region converges to Euler's constant. Euler's constant (sometimes called the Euler–Mascheroni constant) is a mathematical constant, usually denoted by the lowercase Greek letter gamma (γ), defined as the limiting difference between the harmonic series and the natural logarithm, denoted here by log:

  9. Logarithmic number system - Wikipedia

    en.wikipedia.org/wiki/Logarithmic_number_system

    An LNS can be considered as a floating-point number with the significand being always equal to 1 and a non-integer exponent. This formulation simplifies the operations of multiplication, division, powers and roots, since they are reduced down to addition, subtraction, multiplication, and division, respectively.