Binäärilogaritm

Binäärilogaritm, often denoted as lb(x) or log₂(x), is the logarithm to base two. It answers the question of what power must be raised to 2 to equal x. For example, the binäärilogaritm of 8 is 3, because 2³ = 8.

The binäärilogaritm is fundamental in computer science. It is used to measure information content, such as in bits. The number of bits required to represent n distinct values is ⌈lb(n)⌉, where ⌈x⌉ is the ceiling function. This is because each bit can represent two states, so k bits can represent 2ᵏ states.

In mathematics, the binäärilogaritm is a special case of the general logarithm function. It shares the same properties, such as lb(ab) = lb(a) + lb(b) and lb(a/b) = lb(a) - lb(b). It is also related to the natural logarithm (ln) and the common logarithm (log₁₀) by the change of base formula: lb(x) = ln(x) / ln(2) or lb(x) = log₁₀(x) / log₁₀(2).

The function lb(x) is defined for all positive real numbers x. Its graph passes through the point (1, 0) and increases as x increases. It is the inverse function of the exponential function 2ˣ. The binäärilogaritm has applications in various fields, including information theory, digital signal processing, and algorithm analysis.