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  2. Logarithm - Wikipedia

    en.wikipedia.org/wiki/Logarithm

    Exponentiation occurs in many areas of mathematics and its inverse function is often referred to as the logarithm. For example, the logarithm of a matrix is the (multi-valued) inverse function of the matrix exponential. [97] Another example is the p-adic logarithm, the inverse function of the p-adic exponential.

  3. 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.

  4. Inverse function - Wikipedia

    en.wikipedia.org/wiki/Inverse_function

    In mathematics, the inverse function of a function f (also called the inverse of f) is a function that undoes the operation of f. The inverse of f exists if and only if f is bijective , and if it exists, is denoted by f − 1 . {\displaystyle f^{-1}.}

  5. Lambert W function - Wikipedia

    en.wikipedia.org/wiki/Lambert_W_function

    The name "product logarithm" can be understood as this: Since the inverse function of f(w) = e w is called the logarithm, it makes sense to call the inverse "function" of the product we w as "product logarithm". (Technical note: like the complex logarithm, it is multivalued and thus W is described as the converse relation rather than inverse ...

  6. 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 ...

  7. Binary logarithm - Wikipedia

    en.wikipedia.org/wiki/Binary_logarithm

    The binary logarithm function may be defined as the inverse function to the power of two function, which is a strictly increasing function over the positive real numbers and therefore has a unique inverse. [7] Alternatively, it may be defined as ln n/ln 2, where ln is the natural logarithm, defined in any of its standard ways.

  8. Complex logarithm - Wikipedia

    en.wikipedia.org/wiki/Complex_logarithm

    Such complex logarithm functions are analogous to the real logarithm function: >, which is the inverse of the real exponential function and hence satisfies e ln x = x for all positive real numbers x. Complex logarithm functions can be constructed by explicit formulas involving real-valued functions, by integration of 1 / z {\displaystyle 1/z ...

  9. Exponential function - Wikipedia

    en.wikipedia.org/wiki/Exponential_function

    The exponential function is the inverse function of the natural logarithm. The inverse function theorem implies that the natural logarithm has an inverse function, that satisfies the above definition. This is a first proof of existence.