Log28

Log28 denotes the logarithm of a number with base 28. It is the inverse function of the exponential 28^y, so for a positive input x the value y = log28(x) satisfies 28^y = x. In standard notation it is written as log base 28 of x, or log28(x).

Domain and range: The function log28(x) is defined for x > 0 and its range is all real numbers. Since the base 28 is greater than 1, the function is strictly increasing.

Basic properties: For positive x and y, log28(xy) = log28(x) + log28(y), and log28(x^k) = k log28(x). These follow from the corresponding properties of logarithms with any base.

Change of base: log28(x) can be computed using any other logarithm, for example log28(x) = ln(x) / ln(28) or log28(x) = log10(x) / log10(28). This makes log28 accessible with calculators that provide common or natural logarithms.

Examples: log28(28) = 1, log28(1) = 0, and log28(2) ≈ 0.208, log28(7) ≈ 0.584, log28(14) ≈ 0.793. These reflect that 28^1 = 28 and 28^0 = 1, with other values falling between these bounds.

Relation to numbers: Since 28 = 2^2 × 7, the base 28 is not a simple power of a single small integer, so many logarithm values do not simplify to neat fractions. In practice, log28 is most often evaluated via the change-of-base formula using a calculator or software.