Logarithm Function

A Logarithm Function is a Binary Scalar Numeric Function with Arguments (x and b) that returns Number (y) iff x=b^y.

• AKA: Logarithm, Log Function.
• Context:
  • y = log_b(x) iff x=b^y
  • log_b(1) = 0
  • log_b(b) = 1
  • log_b(x*y) = log_b(x) + log_b(y)
  • log_b(x/y) = log_b(x) - log_b(y)
  • log_b(x n) = n log_b(x)
  • log_b(x) = log_b(c) * log_c(x) = log_c(x) / log_c(b)
• Example(s):
  • Natural Logarithm Function.
• See: Power Function, Exponentiation Operation.

References

• (Wikipedia, 2009) http://en.wikipedia.org/wiki/Logarithm
  • In mathematics, the logarithm of a number to a given base is the power or exponent to which the base must be raised in order to produce the number.
  • For example, the logarithm of 1000 to the base 10 is 3, because 3 is how many 10s you must multiply to get 1000: thus 10 × 10 × 10 = 1000; the base 2 logarithm of 32 is 5 because 5 is how many 2s one must multiply to get 32: thus 2 × 2 × 2 × 2 × 2 = 32. In the language of exponents: 103 = 1000, so log101000 = 3, and 25 = 32, so log232 = 5.
  • The logarithm of x to the base b is written log_b(x) or, if the base is implicit, as log(x). So, for a number x, a base b and an exponent y,
    • if x = b^y, then y = log_b (x)\,.
  • An important feature of logarithms is that they reduce multiplication to addition, by the formula:
    • log (xy) = log x + \log y ,.
  • That is, the logarithm of the product of two numbers is the sum of the logarithms of those numbers. The use of logarithms to facilitate complicated calculations was a significant motivation in their original development.
• http://www.math.com/tables/algebra/exponents.htm
  • y = log_b(x) if and only if x=b^y
  • log_b(1) = 0
  • log_b(b) = 1
  • log_b(x*y) = log_b(x) + log_b(y)
  • log_b(x/y) = log_b(x) - log_b(y)
  • log_b(x n) = n log_b(x)
  • logb(x) = logb(c) * logc(x) = logc(x) / logc(b)