# Logarithmic Functions

A series of free, online Intermediate Algebra Lessons or Algebra II lessons.
Examples, solutions, videos, worksheets, and activities to help Algebra students.

In this lesson, we will learn

• how to expand logarithms
• how to condense logarithms
• evaluate logarithms

The following diagram shows some of the log properties that can be used to expand and evaluate logarithms. ### Expanding Logarithms

Sometimes we use methods for expanding logarithms in complicated logarithmic terms. Expanding logarithms can be useful for obtaining more simplified terms. When expanding logarithms we use the rules of logarithms, including the power rule, the product rule and the quotient rule. Sometimes we use methods for expanding logarithms when evaluating logarithmic equations.

### Condensing Logarithms

When evaluating logarithmic equations, we can use methods for condensing logarithms in order to rewrite multiple logarithmic terms into one. Condensing logarithms can be a useful tool for the simplification of logarithmic terms. When condensing logarithms we use the rules of logarithms, including the product rule, the quotient rule and the power rule.

This video shows how to condense multiple logarithms into a single logarithmic expression.

### Evaluating a Logarithmic Expression in terms of Known Quantities

In order to do problems on evaluating logarithms in terms of known quantities, we need to understand the rules of logarithms such as the product, the quotient and the power rules. When we say evaluating logarithms in terms of known quantities, we mean that we want to be able to rewrite a complex logarithm so that we can recognize certain simpler logarithmic terms within it.

How to break up a logarithm of a large number?

Evaluating logs and re-arranging logarithms.

Using log rules to evaluate logarithms.

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