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  2. Laws of exponents - Wikipedia

    en.wikipedia.org/wiki/Laws_of_exponents

    The laws of exponents or exponent laws are a set of mathematical laws for use in the simplification, evaluation, and manipulation of mathematical expressions.

  3. List of logarithmic identities - Wikipedia

    en.wikipedia.org/wiki/List_of_logarithmic_identities

    These are the three main logarithm laws/rules/principles, [3] from which the other properties listed above can be proven. Each of these logarithm properties correspond to their respective exponent law, and their derivations/proofs will hinge on those facts. There are multiple ways to derive/prove each logarithm law – this is just one possible ...

  4. Exponentiation - Wikipedia

    en.wikipedia.org/wiki/Exponentiation

    When an exponent is a positive integer, that exponent indicates how many copies of the base are multiplied together. For example, 3 5 = 3 · 3 · 3 · 3 · 3 = 243. The base 3 appears 5 times in the multiplication, because the exponent is 5. Here, 243 is the 5th power of 3, or 3 raised to the 5th power.

  5. Law (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Law_(mathematics)

    In mathematics, a law is a formula that is always true within a given context. [1] Laws describe a relationship , between two or more expressions or terms (which may contain variables ), usually using equality or inequality , [ 2 ] or between formulas themselves, for instance, in mathematical logic .

  6. Exponential function - Wikipedia

    en.wikipedia.org/wiki/Exponential_function

    Exponential functions with bases 2 and 1/2. In mathematics, the exponential function is the unique real function which maps zero to one and has a derivative equal to its value. . The exponential of a variable ⁠ ⁠ is denoted ⁠ ⁡ ⁠ or ⁠ ⁠, with the two notations used interchangeab

  7. Power rule - Wikipedia

    en.wikipedia.org/wiki/Power_rule

    The power rule for differentiation was derived by Isaac Newton and Gottfried Wilhelm Leibniz, each independently, for rational power functions in the mid 17th century, who both then used it to derive the power rule for integrals as the inverse operation. This mirrors the conventional way the related theorems are presented in modern basic ...

  8. Euler's formula - Wikipedia

    en.wikipedia.org/wiki/Euler's_formula

    In electrical engineering, signal processing, and similar fields, signals that vary periodically over time are often described as a combination of sinusoidal functions (see Fourier analysis), and these are more conveniently expressed as the sum of exponential functions with imaginary exponents, using Euler's formula.

  9. Zipf's law - Wikipedia

    en.wikipedia.org/wiki/Zipf's_law

    Zipf's law can be visuallized by plotting the item frequency data on a log-log graph, with the axes being the logarithm of rank order, and logarithm of frequency. The data conform to Zipf's law with exponent s to the extent that the plot approximates a linear (more precisely, affine) function with slope −s.

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