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...

log x. 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 regularly in various...

{\displaystyle \exp(x+y)=\exp x\cdot \exp y} ⁠. Its inverse function, the natural logarithm, ⁠ ln {\displaystyle \ln } ⁠ or ⁠ log {\displaystyle \log } ⁠, converts...

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...

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...

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...

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

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...

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...

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...

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

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...

{\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...

\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...

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...

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...

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)...

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...

Wonderful Rule of Logarithms). The book contained fifty-seven pages of explanatory matter and ninety pages of tables related to natural logarithms. The English...

Binary logarithm Bode plot Henry Briggs Bygrave slide rule Cologarithm Common logarithm Complex logarithm Discrete logarithm Discrete logarithm records...

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

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

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...

on the chain rule as well as properties of logarithms (in particular, the natural logarithm, or the logarithm to the base e) to transform products into...

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

In physics, optical depth or optical thickness is the natural logarithm of the ratio of incident to transmitted radiant power through a material. Thus...

{\displaystyle g_{0}} is standard gravity; ln {\displaystyle \ln } is the natural logarithm function; m 0 {\displaystyle m_{0}} is the initial total mass, including...