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  2. List of logarithmic identities - Wikipedia

    en.wikipedia.org/wiki/List_of_logarithmic_identities

    The complex logarithm is the complex number analogue of the logarithm function. No single valued function on the complex plane can satisfy the normal rules for logarithms. However, a multivalued function can be defined which satisfies most of the identities. It is usual to consider this as a function defined on a Riemann surface.

  3. Logarithmic growth - Wikipedia

    en.wikipedia.org/wiki/Logarithmic_growth

    Logarithmic growth is the inverse of exponential growth and is very slow. [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] In more advanced mathematics, the partial sums of the harmonic series

  4. Logarithm - Wikipedia

    en.wikipedia.org/wiki/Logarithm

    However, in general settings, the logarithm tends to be a multi-valued function. For example, the complex logarithm is the multi-valued inverse of the complex exponential function. Similarly, the discrete logarithm is the multi-valued inverse of the exponential function in finite groups; it has uses in public-key cryptography.

  5. Natural logarithm - Wikipedia

    en.wikipedia.org/wiki/Natural_logarithm

    The natural logarithm function, if considered as a real-valued function of a positive real variable, is the inverse function of the exponential function, leading to the identities: ⁡ = + ⁡ = Like all logarithms, the natural logarithm maps multiplication of positive numbers into addition: [ 5 ] ln ⁡ ( x ⋅ y ) = ln ⁡ x + ln ⁡ y ...

  6. Exponentiation - Wikipedia

    en.wikipedia.org/wiki/Exponentiation

    The definition of e x as the exponential function allows defining b x for every positive real numbers b, in terms of exponential and logarithm function. Specifically, the fact that the natural logarithm ln(x) is the inverse of the exponential function e x means that one has = ⁡ (⁡) = ⁡ for every b > 0.

  7. Lambert W function - Wikipedia

    en.wikipedia.org/wiki/Lambert_W_function

    The product logarithm Lambert W function plotted in the complex plane from −2 − 2i to 2 + 2i The graph of y = W(x) for real x < 6 and y > −4. The upper branch (blue) with y ≥ −1 is the graph of the function W 0 (principal branch), the lower branch (magenta) with y ≤ −1 is the graph of the function W −1. The minimum value of x is ...

  8. Log-normal distribution - Wikipedia

    en.wikipedia.org/wiki/Log-normal_distribution

    This relationship is true regardless of the base of the logarithmic or exponential function: If ⁡ is normally distributed, then so is ⁡ for any two positive numbers , . Likewise, if e Y {\displaystyle \ e^{Y}\ } is log-normally distributed, then so is a Y , {\displaystyle \ a^{Y}\ ,} where 0 < a ≠ 1 {\displaystyle 0<a\neq 1} .

  9. Euler's formula - Wikipedia

    en.wikipedia.org/wiki/Euler's_formula

    This complex exponential function is sometimes denoted cis x ("cosine plus i sine"). The formula is still valid if x is a complex number, and is also called Euler's formula in this more general case. [1] Euler's formula is ubiquitous in mathematics, physics, chemistry, and engineering.

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