log2value

Log2value is the logarithm of a positive numeric input to base 2, commonly written as log2(x). It answers how many times the number 1 must be doubled to reach x, with log2(1) = 0 and log2(2) = 1. The function is defined for all x > 0 and yields real numbers, and it is strictly increasing on its domain.

Key properties include log2(ab) = log2(a) + log2(b) and log2(a^k) = k log2(a). The change of base formula log2(x) = ln(x) / ln(2) shows how to compute it from other logarithms. log2 is the inverse of the exponential function 2^y; its range is all real numbers and its domain is x > 0.

In computing and computer science, log2value is used to measure data sizes and algorithmic complexity, and to determine the number of bits required to represent a value. For integers, floor(log2(x)) gives the index of the most significant bit, and the bit-length is floor(log2(x)) + 1. Many programming languages provide a built-in log2 function; when unavailable, it can be computed as log(x)/log(2).

Edge cases and variants: the function is undefined for x ≤ 0. Variants such as floor log2, ceil log2, or the bit-length function are common in discrete algorithms and bitwise tasks. Numerical implementations may use approximations for speed or precision constraints.