Log2L

Log2L denotes the base-2 logarithm of a quantity L, typically a positive quantity such as a likelihood function L(θ) or a probability value. By definition, log2 L equals the logarithm of L to base 2; equivalently log2 L = ln L / ln 2. Because the base-2 logarithm is strictly increasing on positive arguments, it preserves the order of L and does not alter the existence of maxima.

With a likelihood function L(θ), maximizing L(θ) over θ is equivalent to maximizing log2 L(θ). The same argmax arises because the logarithm is a monotonically increasing transformation.

Applications and interpretation: In contexts where information is measured in bits or where base-2 units are natural, log2 L provides a natural scale for information content. It can also improve numerical stability by converting products of probabilities or likelihoods into sums. In standard likelihood-based inference, natural logarithm is customary; replacing log base e by log base 2 changes the magnitude of the log-likelihood by a constant factor 1/ln 2, but not the underlying optimization. Consequently, likelihood-ratio statistics computed with log2 L are proportional to the conventional statistics (specifically, 2*(log2 L1 − log2 L0) = (2/ln 2)*(ln L1 − ln L0)).

Examples: If L = 8, log2 L = 3; if L = 0.25, log2 L = −2.

See also: log likelihood, log base, likelihood ratio test, information content.