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...

base b. The logarithm base 10 is called the decimal or common logarithm and is commonly used in science and engineering. The natural logarithm has the number e...

mathematical constant approximately equal to 2.71828 that is the base of the natural logarithm and exponential function. It is sometimes called Euler's number, after...

In mathematics, the natural logarithm of 2 is the unique real number argument such that the exponential function equals two. It appears frequently in...

exponential function is occasionally called the natural exponential function, matching the name natural logarithm, for distinguishing it from some other functions...

the common logarithm (aka "standard logarithm") is the logarithm with base 10. It is also known as the decadic logarithm, the decimal logarithm and the Briggsian...

positive values, this is equal to the derivative of ln(f), or the natural logarithm of f. This follows directly from the chain rule: d d x ln ⁡ f ( x...

In mathematics, a complex logarithm is a generalization of the natural logarithm to nonzero complex numbers. The term refers to one of the following, which...

the natural logarithm function mapping the real numbers to themselves. The logarithm of a non-positive real is not a real number, so the natural logarithm...

equal to 1.380649 × 10−23 J/K, and ln {\displaystyle \ln } is the natural logarithm function (or log base e, as in the image above). In short, the Boltzmann...

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...

\over 3}-{1 \over 4}+{1 \over 5}-\cdots ,} which has a sum of the natural logarithm of 2, while the sum of the absolute values of the terms is the harmonic...

science and engineering until the 1970s. A breakthrough generating the natural logarithm was the result of a search for an expression of area against a rectangular...

numbers b, in terms of exponential and logarithm function. Specifically, the fact that the natural logarithm ln(x) is the inverse of the exponential...

functions. The area of a hyperbolic sector in standard position is natural logarithm of b . Proof: Integrate under 1/x from 1 to b, add triangle {(0, 0)...

Napierian logarithm or Naperian logarithm, named after John Napier, is often used to mean the natural logarithm. Napier did not introduce this natural logarithmic...

the binary iterated logarithm, which iterates the binary logarithm (with base 2 {\displaystyle 2} ) instead of the natural logarithm (with base e). Mathematically...

we find the Maclaurin series of ln(1 − x), where ln denotes the natural logarithm: − x − 1 2 x 2 − 1 3 x 3 − 1 4 x 4 − ⋯ . {\displaystyle -x-{\tfrac...

{\displaystyle e^{ix}=\cos x+i\sin x,} where e is the base of the natural logarithm, i is the imaginary unit, and cos and sin are the trigonometric functions...

natural unit of information (symbol: nat), sometimes also nit or nepit, is a unit of information or information entropy, based on natural logarithms and...

numbers already noted above. The nth derivative of the μth power of the natural logarithm involves the signed Stirling numbers of the first kind: d n ( ln ⁡...

x i {\displaystyle x_{i}} is a sample point in each interval. The natural logarithm ln ⁡ ( 1 + x ) {\displaystyle \ln(1+x)} has a well-known Taylor series...

\ln } is the natural logarithm and γ ≈ 0.577 {\displaystyle \gamma \approx 0.577} is the Euler–Mascheroni constant. Because the logarithm has arbitrarily...

{(-1)^{k+1}}{k}}(z-1)^{k}} is a power series corresponding to the natural logarithm near z = 1. This power series can be turned into a germ g = ( 1 ,...

In mathematics, a logarithm of a matrix is another matrix such that the matrix exponential of the latter matrix equals the original matrix. It is thus...

t_{1/2}={\frac {\ln(2)}{\lambda }}=\tau \ln(2)} where ln(2) is the natural logarithm of 2 (approximately 0.693).: 112  In chemical kinetics, the value...

calculated by taking the natural logarithm ⁠ ln {\displaystyle \ln } ⁠ of each number, finding the arithmetic mean of the logarithms, and then returning the...

series for ex. The Taylor series for the principal branch of the natural logarithm in the neighborhood of 1 is well known: log ⁡ ( 1 + x ) = x − x 2...

The general logarithm, to an arbitrary positive base, Euler presents as the inverse of an exponential function. Then the natural logarithm is obtained...

definition of the constant e {\displaystyle e} , the base of the natural logarithm, now known as Euler's number. Euler made contributions to applied...