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  2. Natural logarithm - Wikipedia

    en.wikipedia.org/wiki/Natural_logarithm

    For example, ln 7.5 is 2.0149..., because e 2.0149... = 7.5. The natural logarithm of e itself, ln e, is 1, because e 1 = e, while the natural logarithm of 1 is 0, since e 0 = 1. The natural logarithm can be defined for any positive real number a as the area under the curve y = 1/x from 1 to a [4] (with the area being negative when 0 < a < 1 ...

  3. List of logarithmic identities - Wikipedia

    en.wikipedia.org/wiki/List_of_logarithmic_identities

    Logarithms can be used to make calculations easier. For example, two numbers can be multiplied just by using a logarithm table and adding. These are often known as logarithmic properties, which are documented in the table below. [2] The first three operations below assume that x = b c and/or y = b d, so that log b (x) = c and log b (y) = d.

  4. Logarithm - Wikipedia

    en.wikipedia.org/wiki/Logarithm

    In mathematics, the logarithm of a number is the exponent by which another fixed value, the base, must be raised to produce that number. For example, the logarithm of 1000 to base 10 is 3, because 1000 is 10 to the 3 rd power: 1000 = 10 3 = 10 × 10 × 10.

  5. e (mathematical constant) - Wikipedia

    en.wikipedia.org/wiki/E_(mathematical_constant)

    The number e is a 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 the Swiss mathematician Leonhard Euler, though this can invite confusion with Euler numbers, or with Euler's constant, a different constant typically denoted .

  6. Prime number theorem - Wikipedia

    en.wikipedia.org/wiki/Prime_number_theorem

    For example, π(10) = 4 because there are four prime numbers (2, 3, 5 and 7) less than or equal to 10. The prime number theorem then states that x / log x is a good approximation to π(x) (where log here means the natural logarithm), in the sense that the limit of the quotient of the two functions π(x) and x / log x as x increases without ...

  7. Euler's identity - Wikipedia

    en.wikipedia.org/wiki/Euler's_identity

    In mathematics, Euler's identity [note 1] (also known as Euler's equation) is the equality + = where . is Euler's number, the base of natural logarithms, is the imaginary unit, which by definition satisfies =, and

  8. 10 Hard Math Problems That Even the Smartest People in the ...

    www.aol.com/10-hard-math-problems-even-150000090...

    It turns out functions like this have certain properties that cast insight into math topics like Algebra and Number Theory. British mathematicians Bryan Birch and Peter Swinnerton-Dyer developed ...

  9. Euler's formula - Wikipedia

    en.wikipedia.org/wiki/Euler's_formula

    Euler's formula is ubiquitous in mathematics, physics, chemistry, and engineering. The physicist Richard Feynman called the equation "our jewel" and "the most remarkable formula in mathematics". [2] When x = π, Euler's formula may be rewritten as e iπ + 1 = 0 or e iπ = −1, which is known as Euler's identity.

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