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The LSE function is often encountered when the usual arithmetic computations are performed on a logarithmic scale, as in log probability. [5]Similar to multiplication operations in linear-scale becoming simple additions in log-scale, an addition operation in linear-scale becomes the LSE in log-scale:
The identities of logarithms can be used to approximate large numbers. Note that log b (a) + log b (c) = log b (ac), where a, b, and c are arbitrary constants. Suppose that one wants to approximate the 44th Mersenne prime, 2 32,582,657 −1. To get the base-10 logarithm, we would multiply 32,582,657 by log 10 (2), getting 9,808,357.09543 ...
The sum of probabilities + is a bit more involved to compute in logarithmic space, requiring the computation of one exponent and one logarithm. However, in many applications a multiplication of probabilities (giving the probability of all independent events occurring) is used more often than their addition (giving the probability of at least ...
The sum of exponentials is a useful model in pharmacokinetics (chemical kinetics in general) for describing the concentration of a substance over time. The exponential terms correspond to first-order reactions, which in pharmacology corresponds to the number of modelled diffusion compartments. [2] [3]
This list of mathematical series contains formulae for finite and infinite sums. It can be used in conjunction with other tools for evaluating sums. Here, is taken to have the value
In mathematics, an elementary function is a function of a single variable (typically real or complex) that is defined as taking sums, products, roots and compositions of finitely many polynomial, rational, trigonometric, hyperbolic, and exponential functions, and their inverses (e.g., arcsin, log, or x 1/n).
The United States Food and Drugs Administration is warning pet owners about a common medication given to pets to treat arthritis. The F.D.A. now says that the drug Librela may be associated with ...
The definition of e x as the exponential function allows defining b x for every positive real numbers b, in terms of exponential and logarithm function. Specifically, the fact that the natural logarithm ln(x) is the inverse of the exponential function e x means that one has = () =