(redirected from Logarithmic function)
Also found in: Dictionary, Thesaurus, Encyclopedia, Wikipedia.


If a number, x, is expressed as a power of another number, y, that is, if x = yn, then n is said to be the logarithm of x to base y. Common logarithms are to the base 10; natural or Napierian logarithms are to the base e, a mathematical constant.
[G. logos, word, ratio, + arithmos, number]


a mathematical device.

common logarithm
the value of the power when a number is expressed as to the power of 10 (has the base 10). Thus 100 expressed as to the power of 10 is 102 and the log of 100 is 2.
Napierian logarithm
see natural logarithm (below).
natural logarithm
as for common logarithm, except that the base is e or 2.178. Called also Napierian logarithm.
References in periodicals archive ?
The controller can be made more accurate by using logarithmic functions within the model description.
The result covers fundamental concepts of algebra, equations and inequalities, functions and graphs, polynomial and rational function, inverse functions, exponential and logarithmic functions, trigonometric functions, analytical trigonometry, applications of trigonometry, systems of equations and inequalities, sequences, series and probability, and topics from analytical geometry.
Twelve chapters cover pre-calculus review, differentiation, exponential and logarithmic functions, probability and calculus, and Taylor polynomials and infinite series, among other topics.
The chapters include a review of basic algebra, systems of equations, rational expressions and equations, exponential and logarithmic functions, and conic sections with more graphing.
They start with real numbers and their basic properties, then turn to equations and inequalities, graphing and solving systems of equations and inequalities, polynomials, factoring polynomials, proportions and rational expressions, writing equations of lines along with functions and variations, radicals and rational exponents, quadratic functions, inequalities, algebra of functions, exponential and logarithmic functions, conic sections and a set of miscellaneous topics such as geometric sequences.
The topics are real numbers and variable expressions, first-degree equations and inequalities, geometry, linear functions and inequalities in two variables, systems of linear equations and inequalities, polynomials, factoring, rational expressions, exponents and radicals, quadratic equations, functions and relations, and exponential and logarithmic functions.
This textbook presents equations as mathematical models, plots straight lines and functions as graphs, and explains how to solve polynomial, rational, quadratic, exponential, and logarithmic functions.
Later chapters cover continuity of functions, derivatives of functions, trigonometric limits, and exponential and logarithmic functions and their derivatives, in addition to implicit functions, parametric functions, Rolle's theorem, Taylor's formula, and hyperbolic functions.
Two instructors at Anoka Ramsey Community College progress through functions and graphs, polynomial and rational functions, logarithmic functions, trigonometric functions, sines and cosines, systems of equations and inequalities, sequences, and probability with a final chapter on analytic geometry.
Among the topics are lines in the plane, trigonometry, numbers, exponential and logarithmic functions, and transcendental functions and complex numbers.
The volume covers all basic precalculus topics including polynomial, rational, exponential and logarithmic functions, trigonometry, linear systems and analytic geometry.