Logarithms - Product Rule

Laws of Logarithms

The Laws of Logarithms or logarithmic rules are crucial for simplifying logarithmic expressions and solving equations involving logarithms.

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

 

Logarithm Worksheets
Practice your Logarithm skills with the following worksheets:
Printable & Online Logarithm Worksheets

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_bx + log_by

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_bx + log_by
Do not be confused: log_b(x + y) ≠ log_bx + log_by

• Show Video Lesson

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. log₂(15x(7x + 2))

• Show Video Lesson

Logarithms - Product Rule of Logs

Examples:
log_b(xy)
log_b(z²y)
log₃81
log_b(x² - 4)

• Show Video Lesson

Expand Logarithmic Expressions

Examples:
Expand each logarithm as much as possible.

1. log₂(x⁴√x⁵)
   
2. ln(x³y²/z⁵)

• Show Video Lesson

More examples on how to expand logarithms.

• Show Video Lesson

Check out our most popular games!

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.