 # Properties of Logarithms

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

In this lesson, we will learn

• the product rule of logarithms
• the quotient rule of logarithms
• the power rule of logarithms

### Product Rule of Logarithms

There are a few rules that can be used when solving logarithmic equations. One of these rules is the logarithmic product rule, which can be used to separate complex logs into multiple terms. Other rules that can be useful are the quotient rule and the power rule of logarithms. The logarithmic product rule is important and is used often in calculus when manipulating logs and simplifying terms for derivation.
Algebra - Logarithms - Product Rule of Logs
How to use the product rule for logarithms.

### Quotient Rule of Logarithms

When evaluating logarithms the logarithmic rules, such as the quotient rule of logarithms, can be useful for rewriting logarithmic terms. The quotient rule of logarithms allows us to separate parts of a quotient within a log. The quotient rule of logarithms is useful for expanding and condensing logarithms, along with the product rule and the power rule of logarithms.
This video is a demonstration of the Quotient Rule of Logarithms.
How to use the quotient rule for logarithms.

### Power Rule of Logarithms

When evaluating logarithmic equations, the logarithm power rule can be a useful tool. The logarithmic power rule can also be used to access exponential terms. When a logarithmic term has an exponent, the logarithm power rule says that we can transfer the exponent to the front of the logarithm. Along with the product rule and the quotient rule, the logarithm power rule can be used for expanding and condensing logarithms.
This lesson shows you what the power rule for logs is, how it works, why it makes sense, and why you might want to use it.
How to use the power rule for logarithms.

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