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The logarithm is denoted "log b x" (pronounced as "the logarithm of x to base b", "the base-b logarithm of x", or most commonly "the log, base b, of x "). An equivalent and more succinct definition is that the function log b is the inverse function to the function x ↦ b x {\displaystyle x\mapsto b^{x}} .
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 ...
An easy way to calculate log 2 n on calculators that do not have a log 2 function is to use the natural logarithm (ln) or the common logarithm (log or log 10) functions, which are found on most scientific calculators. To change the logarithm base to 2 from e, 10, or any other base b, one can use the formulae: [50] [53]
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.
The logarithm keys (log for base-10 and ln for base-e) on a typical scientific calculator. The advent of hand-held calculators largely eliminated the use of common logarithms as an aid to computation. The numerical value for logarithm to the base 10 can be calculated with the following identities: [5]
Modern scientific calculators generally have many more capabilities than the original four- or five-function calculator, and the capabilities differ between manufacturers and models. The capabilities of a modern scientific calculator include: Scientific notation; Floating-point decimal arithmetic; Logarithmic functions, using both base 10 and ...
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 ...
The log-normal distribution has also been associated with other names, such as McAlister, Gibrat and Cobb–Douglas. [4] A log-normal process is the statistical realization of the multiplicative product of many independent random variables, each of which is positive.