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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, loge x, or sometimes, if the base e is implicit, simply log x.
In mathematics, the logarithm is the inverse function to exponentiation. 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 10 {\displaystyle 10} of 1000 is 3 , or log 10 (1000) = 3 .
The decimal value of the natural logarithm of 2 (sequence A002162 in the OEIS ) is approximately. The logarithm of 2 in other bases is obtained with the formula. The common logarithm in particular is ( OEIS : A007524 ) The inverse of this number is the binary logarithm of 10: ( OEIS : A020862 ). By the Lindemann–Weierstrass theorem, the ...
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].
He then called the logarithm, with this number as base, the natural logarithm. As noted by Howard Eves, "One of the anomalies in the history of mathematics is the fact that logarithms were discovered before exponents were in use." Carl B. Boyer wrote, "Euler was among the first to treat logarithms as exponents, in the manner now so familiar."
Logarithmic scale. 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. Unlike a linear scale where each unit of ...
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 ...
A poll of readers conducted by The Mathematical Intelligencer in 1990 named Euler's identity as the "most beautiful theorem in mathematics". In another poll of readers that was conducted by Physics World in 2004, Euler's identity tied with Maxwell's equations (of electromagnetism ) as the "greatest equation ever".