LogC

LogC refers to two related ideas that share a common mathematical root but appear in different contexts. In mathematics, log_C(x) denotes the logarithm of x with base C. It is defined for x > 0 and C > 0 with C ≠ 1, and can be written as log_C(x) = ln(x) / ln(C). Common choices are C = 10 (log base 10) and C = e (the natural logarithm), but any positive base other than 1 is valid. The change-of-base formula holds: log_C(x) = log_k(x) / log_k(C) for any positive k ≠ 1. Key properties include log_C(xy) = log_C(x) + log_C(y) and log_C(x^a) = a log_C(x).

In scientific usage, logC often means the logarithm of a concentration, typically log10([C]). Transforming concentration data with a logarithm helps linearize relationships and stabilize variance in dose–response analyses. When concentrations are zero or fall below detection limits, a standard logarithm is undefined, so researchers may use data handling strategies such as adding a small constant or employing models that accommodate nonpositive values.

Notation varies by field. While log_C(x) is the standard mathematical form, some texts write log(C) or log_C([C]) depending on the context. Importantly, logC is not a universal constant; its meaning depends on the domain: a base of a logarithm in mathematics, or the logarithm of a concentration in scientific data analysis.

See also: logarithm, base change, concentration, dose–response analysis.