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  2. Logarithm - Wikipedia

    en.wikipedia.org/wiki/Logarithm

    The graph of the logarithm function log b (x) (blue) is obtained by reflecting the graph of the function b x (red) at the diagonal line (x = y). As discussed above, the function log b is the inverse to the exponential function x ↦ b x {\displaystyle x\mapsto b^{x}} .

  3. Log–log plot - Wikipedia

    en.wikipedia.org/wiki/Loglog_plot

    In other words, F is proportional to x to the power of the slope of the straight line of its loglog graph. Specifically, a straight line on a loglog plot containing points (x 0, F 0) and (x 1, F 1) will have the function: = ⁡ (/) ⁡ (/), Of course, the inverse is true too: any function of the form = will have a straight line as its log ...

  4. 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 ...

  5. 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 ...

  6. 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 O ( log ∗ ⁡ n ) {\displaystyle O(\log ^{*}n)} .

  7. 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}.}

  8. 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.

  9. 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.