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Binary logarithm. Graph of log2 x as a function of a positive real number x. In mathematics, the binary logarithm (log2 n) is the power to which the number 2 must be raised to obtain the value n. That is, for any real number x, For example, the binary logarithm of 1 is 0, the binary logarithm of 2 is 1, the binary logarithm of 4 is 2, and the ...
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.
Comparison of Linear, Concave, and Convex Functions\nIn original (left) and log10 (right) scales. In science and engineering, a log–log graph or log–log 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 ...
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 ...
Comparison of Stirling's approximation with the factorial. In mathematics, Stirling's approximation (or Stirling's formula) is an asymptotic approximation for factorials. It is a good approximation, leading to accurate results even for small values of . It is named after James Stirling, though a related but less precise result was first stated ...
The method is used because the properties of logarithms provide avenues to quickly simplify complicated functions to be differentiated. [4] These properties can be manipulated after the taking of natural logarithms on both sides and before the preliminary differentiation.
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.
Both the Sudanese Möbius strip and another self-intersecting Möbius strip, the cross-cap, have a circular boundary. A Möbius strip without its boundary, called an open Möbius strip, can form surfaces of constant curvature. Certain highly symmetric spaces whose points represent lines in the plane have the shape of a Möbius strip.