Search results
Results from the WOW.Com Content Network
The natural logarithm of a positive, real number a may be defined as the area under the graph of the hyperbola with equation y = 1/x between x = 1 and x = a. This is the integral [ 4 ] If a is in , then the region has negative area, and the logarithm is negative.
In mathematics, the logarithmto basebis the inverse function of exponentiationwith base b. That means that the logarithm of a number xto the base bis the exponentto which bmust be raised to produce x. For example, since 1000 = 103, the logarithm base 10{\displaystyle 10}of 1000is 3, or log10 (1000) = 3.
Calculus. In mathematics, specifically in calculus and complex analysis, the logarithmic derivative of a function f is defined by the formula where is the derivative of f. [1] Intuitively, this is the infinitesimal relative change in f; that is, the infinitesimal absolute change in f, namely scaled by the current value of f.
ln (r) is the standard natural logarithm of the real number r. Arg (z) is the principal value of the arg function; its value is restricted to (−π, π]. It can be computed using Arg (x + iy) = atan2 (y, x). Log (z) is the principal value of the complex logarithm function and has imaginary part in the range (−π, π].
The Lambert W function is used to solve equations in which the unknown quantity occurs both in the base and in the exponent, or both inside and outside of a logarithm. The strategy is to convert such an equation into one of the form zez = w and then to solve for z using the W function. For example, the equation.
All instances of log (x) without a subscript base should be interpreted as a natural logarithm, also commonly written as ln (x) or loge(x). In mathematics, the prime number theorem (PNT) describes the asymptotic distribution of the prime numbers among the positive integers. It formalizes the intuitive idea that primes become less common as they ...
Comparison of linear, concave, and convex functions when plotted using a linear scale (left) or a log scale (right). 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 ...
List of integrals of logarithmic functions. The following is a list of integrals (antiderivative functions) of logarithmic functions. For a complete list of integral functions, see list of integrals. Note: x > 0 is assumed throughout this article, and the constant of integration is omitted for simplicity.