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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 .
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. Unlike a linear scale where each unit of distance corresponds to the same increment, on a logarithmic scale each ...
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.
Common logarithm. 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 ...
Euler's constant (sometimes called the Euler–Mascheroni constant) is a mathematical constant, usually denoted by the lowercase Greek letter gamma (γ), defined as the limiting difference between the harmonic series and the natural logarithm, denoted here by log: Here, ⌊·⌋ represents the floor function.
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].
Definition and divergence. The harmonic series is the infinite series in which the terms are all of the positive unit fractions. It is a divergent series: as more terms of the series are included in partial sums of the series, the values of these partial sums grow arbitrarily large, beyond any finite limit.
In mathematics, the binary logarithm (log2n) is the power to which the number 2 must be raised to obtain the value n. That is, for any real number x, For example, the binary logarithm of 1 is 0, the binary logarithm of 2 is 1, the binary logarithm of 4 is 2, and the binary logarithm of 32 is 5. The binary logarithm is the logarithm to the base ...