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2. Natural logarithm - Wikipedia

   en.wikipedia.org/wiki/Natural_logarithm

   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 .

3. List of logarithmic identities - Wikipedia

   en.wikipedia.org/wiki/List_of_logarithmic_identities

   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].

4. Logarithm - Wikipedia

   en.wikipedia.org/wiki/Logarithm

   Common logarithms (base 10), historically used in logarithm tables and slide rules, are a basic tool for measurement and computation in many areas of science and engineering; in these contexts log x still often means the base ten logarithm. [10] In mathematics log x usually refers to the natural logarithm (base e). [11]

5. List of mathematical functions - Wikipedia

   en.wikipedia.org/wiki/List_of_mathematical_functions

   Sigma function: Sums of powers of divisors of a given natural number. Euler's totient function: Number of numbers coprime to (and not bigger than) a given one. Prime-counting function: Number of primes less than or equal to a given number. Partition function: Order-independent count of ways to write a given positive integer as a sum of positive ...

6. Arithmetic function - Wikipedia

   en.wikipedia.org/wiki/Arithmetic_function

   Two whole numbers m and n are called coprime if their greatest common divisor is 1, that is, if there is no prime number that divides both of them. Then an arithmetic function a is additive if a(mn) = a(m) + a(n) for all coprime natural numbers m and n; multiplicative if a(1) = 1 and a(mn) = a(m)a(n) for all coprime natural numbers m and n.

7. Legendre's constant - Wikipedia

   en.wikipedia.org/wiki/Legendre's_constant

   All instances of log(x) without a subscript base should be interpreted as a natural logarithm, also commonly written as ln(x) or log e (x). The first 100,000 elements of the sequence a n = log( n ) − n / π ( n ) (red line) appear to converge to a value around 1.08366 (blue line).