Log21SN

Log21SN is a notation used in mathematics and data analysis to denote the base-21 logarithm of a positive quantity SN. In standard form it is written as log_21(SN) and is defined by the equality log_21(SN) = ln(SN)/ln(21). The domain is SN > 0, since the logarithm requires a positive argument.

The base-21 logarithm has several basic properties: log_21(SN^k) = k log_21(SN) for any real k; log_21(1) = 0; and log_21(1/SN) = -log_21(SN). It is the inverse function of the exponential 21^x, meaning that if y = log_21(SN), then SN = 21^y.

Examples help illustrate the concept. If SN = 21, log_21(SN) = 1. If SN = 441, log_21(SN) = 2. If SN = 0.5, log_21(SN) ≈ -0.228, since ln(0.5)/ln(21) is negative.

Usage of log_21(SN) is not common across all disciplines, but it can be employed when SN represents a quantity interpreted on a 21-point scale or when a researcher specifically requires a logarithmic scale with base 21 for data normalization, comparison, or visualization. As with any logarithmic transformation, the choice of base affects scale but not the intrinsic ordering of SN values.

See also: logarithm, change of base, logarithmic scale. Note that log21SN is not a widely standardized notation; its meaning depends on the context in which SN is defined.