Napierian logarithm

Using napierian logarithms (loge = In), Equation (9.27) can be rewritten ... 

A transcendental number, used as the huse ol the system of natural or Napierian logarithms. It is defined hy... 

NEPER (Np), A dimensionless unit for expressing the ratio of two voltages, two currents, or two power values in a logarithmic manner. The number of nepers is the natural (Napierian) logarithm of the square root of the ratio of the two values being compared. Thus, the neper uses the base of 2.71828 in contrast with the bel (or decibel) which uses the common-logarithm base of 10. One neper equals 8.686 decibels. 

The napierian logarithm of the right side of Eq. 6.29b has the large-time limit ... 

In the field of acoustics and signal transmission, signal power levels and signal amplitude levels (or field levels) are usually expressed as the decadic or the napierian logarithm of the ratio of the power P to a reference power P0, or of the field F to a reference field F0. Since power is often proportional to the square of the field or amplitude (when the field acts on equal impedances) it is convenient to define the power level and the field level to be equal in such a case. This is done by... 

R2 refers to the temperature during the contact period of the mbber product with the food or beverage. At a temperature lower than or equal to 130 °C, R2 has a value calculated according to the formula R2 = 0.05e° where e is the base of the natural or Napierian logarithms and T is the contact temperature, expressed in °C. For temperatures higher than 130 °C, R2 always has the value 1.00. 

The logarithmic function that occurs commonly in physics and chemistry as part of the solution to certain differential equations has as its base not the number 10 but the transcendental number e = 2.718 28. To differentiate between the common and the natural or Napierian logarithms, a more explicit notation could be used logio N = x and log N = y, where 10 = N and e = N. In this book, and in many chemistry and physics books, the notation log N is used to indicate the logarithm to the base 10, and In N to indicate the natural logarithm to the base e. 

Logarithms to the base e = 2 71828 are called natural, hyperbolic, or Napierian logarithms. Logarithms to the base 10 are called Briggsian, or common logarithms. 

In this relationship k, is named the Napierian (natural) molar absorption coefficient [1 mol" cm ] of reactant Aj at wavelength of irradiation. In principle the derivation of the kinetic equations becomes easier if exponential functions and Napierian logarithms are involved. For this reason the Napierian units are used first. Division of the relationship above by the volume of the chosen volume element results in... 

Logarithm 16- g9- ri-th9m n. The exponent that indicates the power to which a number is raised to produce a given number. A common logarithm (log) has a base of 10 and a natural (In) or Napierian logarithm has a base of e (irrational number 2.71828...). Conversion of log to In In N= 2.303 logN. 

The true strain, also called the natural strain, denoted by e, takes into account that the initial section A of the material changes with the applied load. It is defined as the Napierian logarithm of the ratio of the actual cross-section area of the sample, A, at a given applied load f to the initial cross-section area A ... 

If the internal frictions are not dependent on the amplitude, then the plot of the Napierian logarithm of the amplitudes versus the number of cycles is linear with a slope equal to the logarithmic decrement. Moreover, during damping of a sound wave, the anelastic behavior leads to a lag between the stress and strain, and the phase angle, 8, between the two waves is then related to the Napierian logarithmic decrement by the simple equation ... 

The physical meaning of the quantities a(A) and K X) can be stated thus the reciprocal of the Napierian coefficient of absorption a(A) corresponds to the thickness of the medium for which the incident intensity is divided by the base of the Napierian logarithm (i.e., e = 2.718281828...), while the reciprocal of the Bunsen-Roscoe coefficient of absorption K X) corresponds to the thickness of the medium for which the incident intensity is divided by ten. In most practical applications the decadic absorption coefficient is used, but the Napierian absorption coefficient is introduced more naturally in theoretical equations. 

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