Logarithms have certain properties depending on interpretations of an equation. The following lists some of the most common properties (these rules are the same for all positive bases):
- loga 1 = 0, because a0 = 1. For example, in the equation 140 = 1, the base is 14 and the exponent is 0. Because a logarithm is an exponent, this would mean the equation can be written as a logarithmic equation, or log14 1 = 0 (zero is the exponent).
- loga a = 1, because a1 = a. For example, in the equation 31 = 3, the base is 3 and the exponent is 1; the result is 3, with the corresponding logarithmic equation being log3 3 = 1.
- loga ax = x, because ax = ax. For example, 34 = 34, with the base as 3. The logarithmic equation becomes log3 34 = 4.