Logarithms have the following properties:

Since a⁰ = 1 and a¹ = a:
Since a^x and log_ax are inverses:
Since a^pa^q = a^p+q and = a^p-q:
Since log_a(Mⁿ) = log_a(M·M·M ^... M) = log_aM + log_aM + log_aM + ^... + log_aM = n·log_aM

Logarithms have an additional property, called property H, and a property H₁ that is a specific case of property H.

The numerous properties listed on this page can be used to evaluate logarithmic functions. Property H₁ is especially useful when evaluating logarithms with a calculator: since most calculators only evaluate logarithms with base 10, we can evaluate log_aM by evaluating . For example, log₃4 = .

Example:

log₅10 + log₅20 - log₅8 =?