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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 = 103, the logarithm base of 1000 is 3, or log10 (1000) = 3.
The natural logarithm of e itself, ln e, is 1, because e1 = e, while the natural logarithm of 1 is 0, since e0 = 1. The natural logarithm can be defined for any positive real number a as the area under the curve y = 1/x from 1 to a[4] (with the area being negative when 0 < a < 1). The simplicity of this definition, which is matched in many ...
Comparison of Linear, Concave, and Convex Functions\nIn original (left) and log10 (right) scales. 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 – appear as straight ...
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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].
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In mathematics, a parent function is the core representation of a function type without manipulations such as translation and dilation. [1] For example, for the family of quadratic functions having the general form. the simplest function is. This is therefore the parent function of the family of quadratic equations.