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  2. Logarithm - Wikipedia

    en.wikipedia.org/wiki/Logarithm

    In mathematics, the logarithm to baseb is the inverse function of exponentiation with base b. That means that the logarithm of a number x to the base b is the exponent to which b must be raised to produce x. For example, since 1000 = 103, the logarithm base of 1000 is 3, or log10(1000) = 3.

  3. Log–log plot - Wikipedia

    en.wikipedia.org/wiki/Loglog_plot

    Comparison of Linear, Concave, and Convex Functions\nIn original (left) and log10 (right) scales. In science and engineering, a loglog graph or loglog plot is a two-dimensional graph of numerical data that uses logarithmic scales on both the horizontal and vertical axes. Power functions – relationships of the form – appear as straight ...

  4. Iterated logarithm - Wikipedia

    en.wikipedia.org/wiki/Iterated_logarithm

    The iterated logarithm is closely related to the generalized logarithm function used in symmetric level-index arithmetic. The additive persistence of a number, the number of times someone must replace the number by the sum of its digits before reaching its digital root, is . In computational complexity theory, Santhanam [6] shows that the ...

  5. Logarithmic scale - Wikipedia

    en.wikipedia.org/wiki/Logarithmic_scale

    Semi-log plot of the Internet host count over time shown on a logarithmic scale. A logarithmic scale (or log scale) is a method used to display numerical data that spans a broad range of values, especially when there are significant differences between the magnitudes of the numbers involved. Unlike a linear scale where each unit of distance ...

  6. Inverse trigonometric functions - Wikipedia

    en.wikipedia.org/wiki/Inverse_trigonometric...

    A right triangle with sides relative to an angle at the point. Inverse trigonometric functions are useful when trying to determine the remaining two angles of a right triangle when the lengths of the sides of the triangle are known. Recalling the right-triangle definitions of sine and cosine, it follows that.

  7. Natural logarithm - Wikipedia

    en.wikipedia.org/wiki/Natural_logarithm

    The natural logarithm of e itself, ln e, is 1, because e1 = e, while the natural logarithm of 1 is 0, since e0 = 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 ...

  8. Log-normal distribution - Wikipedia

    en.wikipedia.org/wiki/Log-normal_distribution

    This is justified by considering the central limit theorem in the log domain (sometimes called Gibrat's law). The log-normal distribution is the maximum entropy probability distribution for a random variate X —for which the mean and variance of ln (X) are specified.

  9. List of logarithmic identities - Wikipedia

    en.wikipedia.org/wiki/List_of_logarithmic_identities

    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].