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The natural logarithm of a number is its logarithm to the base of the mathematical constant e, which is an irrational and transcendental number approximately equal to 2.718 281 828 459. [1] The natural logarithm of x is generally written as ln x, loge x, or sometimes, if the base e is implicit, simply log x.
Relaxation (physics) In the physical sciences, relaxation usually means the return of a perturbed system into equilibrium . Each relaxation process can be categorized by a relaxation time τ. The simplest theoretical description of relaxation as function of time t is an exponential law exp (−t/τ) ( exponential decay ).
s −1. The becquerel ( / ˌbɛkəˈrɛl /; symbol: Bq) is the unit of radioactivity in the International System of Units (SI). One becquerel is defined as an activity of one decay per second. For applications relating to human health this is a small quantity, [1] and SI multiples of the unit are commonly used. [2]
The Taylor series can be used to calculate the value of an entire function at every point, if the value of the function, and of all of its derivatives, are known at a single point. Uses of the Taylor series for analytic functions include: The partial sums (the Taylor polynomials) of the series can be used as approximations of the function ...
The plateau principle is a mathematical model or scientific law originally developed to explain the time course of drug action ( pharmacokinetics ). [1] The principle has wide applicability in pharmacology, physiology, nutrition, biochemistry, and system dynamics. It applies whenever a drug or nutrient is infused or ingested at a relatively ...
Rate equation. In chemistry, the rate equation (also known as the rate law or empirical differential rate equation) is an empirical differential mathematical expression for the reaction rate of a given reaction in terms of concentrations of chemical species and constant parameters (normally rate coefficients and partial orders of reaction) only ...
Refractive index. A ray of light being refracted through a glass slab. In optics, the refractive index (or refraction index) of an optical medium is a dimensionless number that gives the indication of the light bending ability of that medium. Refraction of a light ray. The refractive index determines how much the path of light is bent, or ...
This extended exponential function still satisfies the exponential identity, and is commonly used for defining exponentiation for complex base and exponent. Powers via logarithms. 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.
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