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):

• log_a 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).
• log_a 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.
• log_a a^x = x, because a^x = a^x. For example, 3⁴ = 3⁴, with the base as 3. The logarithmic equation becomes log₃ 3⁴ = 4.