Properties of Logarithms

Basic Properties All logarithmic functions have certain properties. The basic properties are:

Change of Base Formula One property of logarithms is that a logarithm in any base can be rewritten as an equivalent logarithm in any other base. The formula is: This is known as the change of base formula and is especially useful when the base we are changing to is either 10 (the common log) or e (the natural logarithm) because most calculators have one or both of those logarithm functions built in.

Practice Problem Evaluate: Rewrite the log expression as one using either the common log or the natural log and use your calculator to solve.

Properties A logarithm in any base has the following properties:

Practice Expand each the following expressions as the sum, difference and/or constant multiple of individual logarithms:

Practice Condense each of the following expressions to the logarithm of a single quantity.

Summary