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2. Symbolab - Wikipedia

   en.wikipedia.org/wiki/Symbolab

   Symbolab is an answer engine [1] that provides step-by-step solutions to mathematical problems in a range of subjects. [2] It was originally developed by Israeli start-up company EqsQuest Ltd., under whom it was released for public use in 2011. In 2020, the company was acquired by American educational technology website Course Hero. [3] [4]

3. List of logarithmic identities - Wikipedia

   en.wikipedia.org/wiki/List_of_logarithmic_identities

   The identities of logarithms can be used to approximate large numbers. Note that log b (a) + log b (c) = log b (ac), where a, b, and c are arbitrary constants. Suppose that one wants to approximate the 44th Mersenne prime, 2 32,582,657 −1. To get the base-10 logarithm, we would multiply 32,582,657 by log 10 (2), getting 9,808,357.09543 ...

4. List of limits - Wikipedia

   en.wikipedia.org/wiki/List_of_limits

   Toggle Logarithmic functions subsection. 4.1 Natural logarithms. 4.2 Logarithms to arbitrary bases. ... This can be derived from Viète's formula for ...

5. Logarithm - Wikipedia

   en.wikipedia.org/wiki/Logarithm

   In mathematics, the logarithm to base b is the inverse function of exponentiation with base b. 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 of 1000 is 3, or log 10 (1000) = 3.

6. Prime-counting function - Wikipedia

   en.wikipedia.org/wiki/Prime-counting_function

   The formula is valid for values of x greater than one, which is the region of interest. The sum over the roots is conditionally convergent, and should be taken in order of increasing absolute value of the imaginary part. Note that the same sum over the trivial roots gives the last subtrahend in the formula. For Π 0 (x) we have a more ...

7. Common logarithm - Wikipedia

   en.wikipedia.org/wiki/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 standard logarithm.

8. Stirling's approximation - Wikipedia

   en.wikipedia.org/wiki/Stirling's_approximation

   In mathematics, Stirling's approximation (or Stirling's formula) is an asymptotic approximation for factorials. It is a good approximation, leading to accurate results even for small values of n {\displaystyle n} .

9. Prime number theorem - Wikipedia

   en.wikipedia.org/wiki/Prime_number_theorem

   The first such distribution found is π(N) ~ ⁠ N / log(N) ⁠, where π(N) is the prime-counting function (the number of primes less than or equal to N) and log(N) is the natural logarithm of N. This means that for large enough N , the probability that a random integer not greater than N is prime is very close to 1 / log( N ) .