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Videos, examples, solutions, worksheets, games and activities to help Algebra students learn about the product rule in logarithms.

The following table gives the logarithm rules. Scroll down the page for examples and solutions for the Product Rule.

**What is the Product Rule of Logarithms?**

The log of a product is equal to the sum of the logs of its factors.

log_{b}(xy) = log_{b}x + log_{b}y

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.

**How to use the product rule for logarithms?**

log_{b}(xy) = log_{b}x + log_{b}y

Do not be confused: log_{b}(x + y) ≠ log_{b}x + log_{b}y

**How to expand Logarithms using the Product Rule for Logs?**

Examples:

Use the product rule for logarithms to rewrite the logarithm of a product as the sum of logarithms of its factors.

1. log_{b}(2xyz)

2. log_{2}(15x(7x + 2))

**Logarithms - Product Rule of Logs**

Examples:

log_{b}(xy)

log_{b}(z^{2}y)

log_{3}81

log_{b}(x^{2} - 4)

**Expand Logarithmic Expressions**

Examples:

Expand each logarithm as much as possible.

1. log_{2}(x^{4}√x^{5})

2. ln(x^{3}y^{2}/z^{5})
**More examples on how to expand logarithms.**

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

More Lessons for Grade 9

Math Worksheets

Videos, examples, solutions, worksheets, games and activities to help Algebra students learn about the product rule in logarithms.

The following table gives the logarithm rules. Scroll down the page for examples and solutions for the Product Rule.

The log of a product is equal to the sum of the logs of its factors.

log

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.

log

Do not be confused: log

Examples:

Use the product rule for logarithms to rewrite the logarithm of a product as the sum of logarithms of its factors.

1. log

2. log

Examples:

log

log

log

log

Examples:

Expand each logarithm as much as possible.

1. log

2. ln(x

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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