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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 y = a x k {\displaystyle y=ax^{k}} – appear as straight lines in a log–log graph, with the exponent corresponding to ...
History. The chart was designed by Ian Bailey and Jan E. Lovie-Kitchin at the National Vision Research Institute of Australia. They described their motivation for designing the LogMAR chart as follows: "We have designed a series of near vision charts in which the typeface, size progression, size range, number of words per row and spacings were chosen in an endeavour to achieve a ...
In probability theory, a log-normal (or lognormal) distribution is a continuous probability distribution of a random variable whose logarithm is normally distributed. Thus, if the random variable X is log-normally distributed, then Y = ln (X) has a normal distribution. [2] [3] Equivalently, if Y has a normal distribution, then the exponential ...
Common logarithm. A graph of the common logarithm of numbers from 0.1 to 100. In mathematics, the common logarithm is the logarithm with base 10. [1] It is also known as the decadic logarithm and as the decimal logarithm, named after its base, or Briggsian logarithm, after Henry Briggs, an English mathematician who pioneered its use, as well as ...
In algebraic geometry, a log structure provides an abstract context to study semistable schemes, and in particular the notion of logarithmic differential form and the related Hodge-theoretic concepts. This idea has applications in the theory of moduli spaces, in deformation theory and Fontaine's p-adic Hodge theory, among others.
Log probability. In probability theory and computer science, a log probability is simply a logarithm of a probability. [1] The use of log probabilities means representing probabilities on a logarithmic scale , instead of the standard unit interval . Since the probabilities of independent events multiply, and logarithms convert multiplication to ...
A logarithmically convex function f is a convex function since it is the composite of the increasing convex function and the function , which is by definition convex. However, being logarithmically convex is a strictly stronger property than being convex. For example, the squaring function is convex, but its logarithm is not.
Log-t or Log-Student t. In probability theory, a log-t distribution or log-Student t distribution is a probability distribution of a random variable whose logarithm is distributed in accordance with a Student's t-distribution. If X is a random variable with a Student's t-distribution, then Y = exp ( X) has a log-t distribution; likewise, if Y ...
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