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  2. 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 ...

  3. Logarithm - Wikipedia

    en.wikipedia.org/wiki/Logarithm

    In mathematics, the logarithm of a number is the exponent by which another fixed value, the base, must be raised to produce that number. For example, the logarithm of 1000 to base 10 is 3, because 1000 is 10 to the 3 rd power: 1000 = 10 3 = 10 × 10 × 10.

  4. Logarithmic growth - Wikipedia

    en.wikipedia.org/wiki/Logarithmic_growth

    In mathematics, logarithmic growth describes a phenomenon whose size or cost can be described as a logarithm function of some input. e.g. y = C log (x). Any logarithm base can be used, since one can be converted to another by multiplying by a fixed constant. [1] Logarithmic growth is the inverse of exponential growth and is very slow. [2]

  5. Napierian logarithm - Wikipedia

    en.wikipedia.org/wiki/Napierian_logarithm

    A plot of the Napierian logarithm for inputs between 0 and 10 8. The 19 degree pages from Napier's 1614 table of logarithms of trigonometric functions Mirifici Logarithmorum Canonis Descriptio. The term Napierian logarithm or Naperian logarithm, named after John Napier, is often used to mean the natural logarithm.

  6. Logarithmic - Wikipedia

    en.wikipedia.org/wiki/Logarithmic

    Logarithm, a transcendental function in mathematics; Logarithmic scale, the use of the logarithmic function to describe measurements; Logarithmic spiral, Logarithmic growth; Logarithmic distribution, a discrete probability distribution; Natural logarithm

  7. Tetration - Wikipedia

    en.wikipedia.org/wiki/Tetration

    In 2017, it was proven [15] that there exists a unique function F which is a solution of the equation F(z + 1) = exp(F(z)) and satisfies the additional conditions that F(0) = 1 and F(z) approaches the fixed points of the logarithm (roughly 0.318 ± 1.337i) as z approaches ±i∞ and that F is holomorphic in the whole complex z-plane, except the ...

  8. Complex logarithm - Wikipedia

    en.wikipedia.org/wiki/Complex_logarithm

    A single branch of the complex logarithm. The hue of the color is used to show the argument of the complex logarithm. The brightness of the color is used to show the modulus of the complex logarithm. The real part of log(z) is the natural logarithm of | z |. Its graph is thus obtained by rotating the graph of ln(x) around the z-axis.

  9. Natural logarithm of 2 - Wikipedia

    en.wikipedia.org/wiki/Natural_logarithm_of_2

    In a third layer, the logarithms of rational numbers r = ⁠ a / b ⁠ are computed with ln(r) = ln(a) − ln(b), and logarithms of roots via ln n √ c = ⁠ 1 / n ⁠ ln(c).. The logarithm of 2 is useful in the sense that the powers of 2 are rather densely distributed; finding powers 2 i close to powers b j of other numbers b is comparatively easy, and series representations of ln(b) are ...

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