Knowra Binary logarithm Binary logarithm The logarithm to base 2 of a number: the exponent to which 2 must be raised to obtain that number. It is written log₂(x) and is defined for positive real x.
Exponentiation : The operation of raising a number to a power, such as 2³ = 8. A binary logarithm reverses raising 2 to an exponent.
Information theory : The mathematical study of information, its representation, compression, and transmission. Binary logarithms measure information in bits when outcomes are equally likely.
Common logarithm : A logarithm with base 10, commonly written log(x). It counts powers of ten rather than powers of two.
Power of two : A number of the form 2ⁿ, where n is an integer. Binary logarithms of powers of two return their exponents exactly.
Change of base formula : The identity logₐ(x) = logᵦ(x) / logᵦ(a), which expresses logarithms in one base using another. It lets calculators evaluate base-2 logarithms using common or natural logarithms.
Shannon entropy : A measure of uncertainty in a probability distribution, calculated as the expected information of its outcomes. Its formula uses log₂ when uncertainty is measured in bits.
Natural logarithm : A logarithm with base e, written ln(x), where e is approximately 2.71828. Its calculus properties distinguish it from the base-2 logarithm used in binary counting.
Inverse function : A function that reverses the action of another function on its range. The base-2 logarithm reverses the exponential function with base 2.
Logarithm laws : Identities describing how logarithms interact with products, quotients, and powers. These rules make binary logarithms of multiplied or powered quantities easy to simplify.
Binary numeral system : A positional number system that represents values using the digits 0 and 1. The number of binary digits needed to represent an integer is governed by its base-2 logarithm.
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