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The natural logarithm of a number is its logarithm to the base of the mathematical constant e, which is an irrational and transcendental number approximately equal to 2.718 281 828 459. [1] The natural logarithm of x is generally written as ln x , log e x , or sometimes, if the base e is implicit, simply log x .
Given a positive real number b such that b ≠ 1, the logarithm of a positive real number x with respect to base b [nb 1] is the exponent by which b must be raised to yield x. In other words, the logarithm of x to base b is the unique real number y such that =. [3]
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].
A similar LNS named "signed logarithmic number system" (SLNS) was described in 1975 by Earl Swartzlander and Aristides Alexopoulos; rather than use two's complement notation for the logarithms, they offset them (scale the numbers being represented) to avoid negative logs. [3]
A graph of the common logarithm of numbers from 0.1 to 100. In mathematics, the common logarithm is the logarithm with base 10. [1] It is also known as the decadic logarithm and as the decimal logarithm, named after its base, or Briggsian logarithm, after Henry Briggs, an English mathematician who pioneered its use, as well as standard logarithm.
Graph of log 2 x as a function of a positive real number x. In mathematics, the binary logarithm (log 2 n) is the power to which the number 2 must be raised to obtain the value n. That is, for any real number x, = =.
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Semi-log plot of the Internet host count over time shown on a logarithmic scale. A logarithmic scale (or log scale) is a method used to display numerical data that spans a broad range of values, especially when there are significant differences between the magnitudes of the numbers involved.