The decibel is a relative unit of measurement equal to one tenth of a bel (B). It expresses the ratio of two values of a power or root-power quantity on a logarithmic scale. Two signals whose levels differ by one decibel have a power ratio of 101/10 or root-power ratio of 101/20.
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. The logarithm of x to base b is denoted as logb (x), or without parentheses, logb x. When the base is clear from the context or is irrelevant it is sometimes written log x.
Order of magnitude is a concept used to discuss the scale of numbers in relation to one another.
Benford's law, also known as the Newcomb–Benford law, the law of anomalous numbers, or the first-digit law, is an observation that in many real-life sets of numerical data, the leading digit is likely to be small. In sets that obey the law, the number 1 appears as the leading significant digit about 30% of the time, while 9 appears as the leading significant digit less than 5% of the time. Uniformly distributed digits would each occur about 11.1% of the time. Benford's law also makes predictions about the distribution of second digits, third digits, digit combinations, and so on.
The neper is a logarithmic unit for ratios of measurements of physical field and power quantities, such as gain and loss of electronic signals. The unit's name is derived from the name of John Napier, the inventor of logarithms. As is the case for the decibel and bel, the neper is a unit defined in the international standard ISO 80000. It is not part of the International System of Units (SI), but is accepted for use alongside the SI.
In electrical engineering and control theory, a Bode plot is a graph of the frequency response of a system. It is usually a combination of a Bode magnitude plot, expressing the magnitude of the frequency response, and a Bode phase plot, expressing the phase shift.
The phon is a logarithmic unit of loudness level for tones and complex sounds. Loudness is measured in sones, a linear unit. Human sensitivity to sound is variable across different frequencies; therefore, although two different tones may present an identical sound pressure to a human ear, they may be psychoacoustically perceived as differing in loudness. The purpose of the phon is to provide a logarithmic measurement for perceived sound magnitude, while the primary loudness standard methods result in a linear representation. A sound with a loudness of 1 sone is judged equally loud as a 1 kHz tone with a sound pressure level of 40 decibels above 20 micropascals. The phon is psychophysically matched to a reference frequency of 1 kHz. In other words, the phon matches the sound pressure level (SPL) in decibels of a similarly perceived 1 kHz pure tone. For instance, if a sound is perceived to be equal in intensity to a 1 kHz tone with an SPL of 50 dB, then it has a loudness of 50 phons, regardless of its physical properties. The phon was proposed in DIN 45631 and ISO 532 B by Stanley Smith Stevens.
In mathematics, the binary logarithm is the power to which the number 2 must be raised to obtain the value n. That is, for any real number x,
The Weber–Fechner laws are two related scientific laws in the field of psychophysics, known as Weber's law and Fechner's law. Both relate to human perception, more specifically the relation between the actual change in a physical stimulus and the perceived change. This includes stimuli to all senses: vision, hearing, taste, touch, and smell.
This is a list of logarithm topics, by Wikipedia page. See also the list of exponential topics.
In industrial design, preferred numbers are standard guidelines for choosing exact product dimensions within a given set of constraints. Product developers must choose numerous lengths, distances, diameters, volumes, and other characteristic quantities. While all of these choices are constrained by considerations of functionality, usability, compatibility, safety or cost, there usually remains considerable leeway in the exact choice for many dimensions.
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 lines in a log–log graph, with the exponent corresponding to the slope, and the coefficient corresponding to the intercept. Thus these graphs are very useful for recognizing these relationships and estimating parameters. Any base can be used for the logarithm, though most commonly base 10 are used.
One decade is a unit for measuring ratios on a logarithmic scale, with one decade corresponding to a ratio of 10 between two numbers.
In science and engineering, a semi-log plot/graph or semi-logarithmicplot/graph has one axis on a logarithmic scale, the other on a linear scale. It is useful for data with exponential relationships, where one variable covers a large range of values.
In statistics, data transformation is the application of a deterministic mathematical function to each point in a data set—that is, each data point zi is replaced with the transformed value yi = f(zi), where f is a function. Transforms are usually applied so that the data appear to more closely meet the assumptions of a statistical inference procedure that is to be applied, or to improve the interpretability or appearance of graphs.
The International System of Quantities (ISQ) is a standard system of quantities used in physics and in modern science in general. It includes basic quantities such as length and mass and the relationships between those quantities. This system underlies the International System of Units (SI) but does not itself determine the units of measurement used for the quantities.
In electronics, an octave is a logarithmic unit for ratios between frequencies, with one octave corresponding to a doubling of frequency. For example, the frequency one octave above 40 Hz is 80 Hz. The term is derived from the Western musical scale where an octave is a doubling in frequency. Specification in terms of octaves is therefore common in audio electronics.
In statistics, a misleading graph, also known as a distorted graph, is a graph that misrepresents data, constituting a misuse of statistics and with the result that an incorrect conclusion may be derived from it.
In science and engineering, a power level and a field level are logarithmic magnitudes of certain quantities referenced to a standard reference value of the same type.
In mathematics, the set of positive real numbers, is the subset of those real numbers that are greater than zero. The non-negative real numbers, also include zero. Although the symbols and are ambiguously used for either of these, the notation or for and or for has also been widely employed, is aligned with the practice in algebra of denoting the exclusion of the zero element with a star, and should be understandable to most practicing mathematicians.
