Search results
Results from the WOW.Com Content Network
Any logarithm base can be used, since one can be converted to another by multiplying by a fixed constant. [1] Logarithmic growth is the inverse of exponential growth and is very slow. [2] A familiar example of logarithmic growth is a number, N, in positional notation, which grows as log b (N), where b is the base of the number system used, e.g ...
The standard logistic function is the logistic function with parameters =, =, =, which yields = + = + = / / + /.In practice, due to the nature of the exponential function, it is often sufficient to compute the standard logistic function for over a small range of real numbers, such as a range contained in [−6, +6], as it quickly converges very close to its saturation values of 0 and 1.
The polar equation for a golden spiral is the same as for other logarithmic spirals, but with a special value of the growth factor b: [10] = or = (/), with e being the base of natural logarithms, a being the initial radius of the spiral, and b such that when θ is a right angle (a quarter turn in either direction): =.
Logarithmic spiral (pitch 10°) A section of the Mandelbrot set following a logarithmic spiral. A logarithmic spiral, equiangular spiral, or growth spiral is a self-similar spiral curve that often appears in nature. The first to describe a logarithmic spiral was Albrecht Dürer (1525) who called it an "eternal line" ("ewige Linie").
Exponential growth is the inverse of logarithmic growth. Not all cases of growth at an always increasing rate are instances of exponential growth. For example the function f ( x ) = x 3 {\textstyle f(x)=x^{3}} grows at an ever increasing rate, but is much slower than growing exponentially.
In mathematics, the logarithm to base b is the inverse function of exponentiation with base b. That means that the logarithm of a number x to the base b is the exponent to which b must be raised to produce x. For example, since 1000 = 10 3, the logarithm base of 1000 is 3, or log 10 (1000) = 3.
Get AOL Mail for FREE! Manage your email like never before with travel, photo & document views. Personalize your inbox with themes & tabs. You've Got Mail!
Logarithms can be used to make calculations easier. For example, two numbers can be multiplied just by using a logarithm table and adding. These are often known as logarithmic properties, which are documented in the table below. [2] The first three operations below assume that x = b c and/or y = b d, so that log b (x) = c and log b (y) = d.