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  2. Natural logarithm - Wikipedia

    en.wikipedia.org/wiki/Natural_logarithm

    The natural logarithm of e itself, ln e, is 1, because e 1 = e, while the natural logarithm of 1 is 0, since e 0 = 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 ...

  3. Logarithm - Wikipedia

    en.wikipedia.org/wiki/Logarithm

    The derivative of ln(x) is 1/x; this implies that ln(x) is the unique antiderivative of 1/x that has the value 0 for x = 1. It is this very simple formula that motivated to qualify as "natural" the natural logarithm; this is also one of the main reasons of the importance of the constant e .

  4. e (mathematical constant) - Wikipedia

    en.wikipedia.org/wiki/E_(mathematical_constant)

    They all pass through the point (0,1), but the red line (which has slope 1) is tangent to only e x there. The value of the natural log function for argument e, i.e. ln e, equals 1. The principal motivation for introducing the number e, particularly in calculus, is to perform differential and integral calculus with exponential functions and ...

  5. List of logarithmic identities - Wikipedia

    en.wikipedia.org/wiki/List_of_logarithmic_identities

    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].

  6. Logarithmic number system - Wikipedia

    en.wikipedia.org/wiki/Logarithmic_number_system

    An LNS can be considered as a floating-point number with the significand being always equal to 1 and a non-integer exponent. This formulation simplifies the operations of multiplication, division, powers and roots, since they are reduced down to addition, subtraction, multiplication, and division, respectively.

  7. History of logarithms - Wikipedia

    en.wikipedia.org/wiki/History_of_logarithms

    By use of the geometric series with its conditional radius of convergence, an alternating series called the Mercator series expresses the logarithm function over the interval (0,2). Since the series is negative in (0,1), the "area under the hyperbola" must be considered negative there, so a signed area determines the hyperbolic logarithm.

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  9. Logit - Wikipedia

    en.wikipedia.org/wiki/Logit

    If p is a probability, then p/(1 − p) is the corresponding odds; the logit of the probability is the logarithm of the odds, i.e.: ⁡ = ⁡ = ⁡ ⁡ = ⁡ = ⁡ (). The base of the logarithm function used is of little importance in the present article, as long as it is greater than 1, but the natural logarithm with base e is the one most often used.