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...

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)...

\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...

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...

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

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

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 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...

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

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...

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...

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

{\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...

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...

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...

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

21 Mar 2022 Jordan Ranous Natural logarithm of 2 0.69314... 3 000 000 000 100 13 Feb 2024 Jordan Ranous Natural logarithm of 10 2.30258... 1 200 000...

equality). (In an alternative interpretation of it, Theil-L is the natural-logarithm of the geometric-mean of the ratio: (mean income)/(income i), over...

{\displaystyle K} is a scale factor, and ln {\displaystyle \ln } is the natural logarithm. Some log amps may mirror negative input with positive input (even...

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