Logab

Logab is a nonstandard or informal notation that has appeared in some mathematical and computational texts as a possible shorthand for the logarithm of a number b with base a. The standard notation for this concept is log base a of b, written as log_a(b). Because logab is not part of formal notation, its meaning can vary between authors, calculators, and programming environments.

In plain-text or quick-notes contexts, logab is sometimes intended to denote log_a(b) to avoid subscripts or parentheses. However, in other contexts logab can be read as log(a·b) (the logarithm of the product) or as two separate expressions, log(a) and b, depending on spacing and conventions. Because of this ambiguity, most formal references and documentation prefer explicit notation to prevent misinterpretation.

Examples illustrate the ambiguity. If logab denotes log base a of b, then logab with a = 2 and b = 8 equals log_2(8) = 3. If read as log(a·b) with a = 2 and b = 8, it would be log(16), whose value depends on the chosen base—for example, ln(16) ≈ 2.7726 or log10(16) ≈ 1.2041.

In software and calculators, base-specific logarithms are typically implemented in ways that avoid ambiguity, such as functions that take an explicit base or that apply the change-of-base formula: log_b(x) = log(x)/log(b). See also: logarithm, change of base formula, mathematical notation.