log2G

Log2G, written as log2 G or log2(G), denotes the logarithm of a positive quantity G with base 2. It equals the exponent x such that 2^x = G. The domain is G > 0; the logarithm is undefined for nonpositive inputs. The function is monotone increasing and maps (0, ∞) onto (−∞, ∞). Its inverse is the power function 2^x.

Key properties include:

- log2(G1 G2) = log2 G1 + log2 G2

- log2(G^k) = k log2 G

- log2(G1 / G2) = log2 G1 − log2 G2

- Change of base: log2 G = ln G / ln 2

These identities allow manipulation of products, powers, and quotients within the base-2 logarithmic framework. For integer inputs G > 0, log2 G represents the exponent needed to reach G by repeated doubling.

Examples help illustrate the concept: log2 1 = 0, log2 2 = 1, log2 8 = 3, log2 0.5 = −1, and log2 3 ≈ 1.585. If G is a positive integer, floor(log2 G) gives the position of the most significant set bit, while floor(log2 G) + 1 corresponds to the number of bits required to represent G in binary.

Applications are common in fields that analyze growth in powers of two. In computer science, log2 G often describes algorithmic or data-structure complexity, especially when input sizes scale by powers of two. In information theory, logarithms base 2 measure information in bits, and log2 G frequently appears in formulas involving entropy and probability. Overall, log2 G provides a concise way to express binary-scale growth and measurement.