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Videos, worksheets, examples, solutions, and activities to help Algebra students learn how to simplify or combine or condense logarithmic expressions using the properties of logarithm.

The following table gives the Logarithmic Properties. Scroll down the page for more examples and solutions.

**Combining Logarithmic Expressions**

How to condense or combine a logarithmic expression into a single logarithm using the properties of logarithms?

Examples:

Combine into a single logarithm.

2log_{5}x + 3log_{5}2

2log 8 - 3log 2

**How to condense or combine a logarithmic expression into a single logarithm using the properties of logarithms?**

Examples:

Combine into a single logarithm.

5ln x + 1/2 ln y - 7 ln z

4log 2 - 2log 3 - log 4

**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.

Properties of Logs - Simplify Expression

Apply the properties of logarithms to write a single expression.

Examples:

Write as a single expression.

1. log √2 + log_{3}√2

2. ln 33 - ln 3

**How to condense multiple logarithms into a single logarithmic expression?**

Examples:

1/2 log_{8} x + 3 log_{8} (x + 1)

2 ln (x + 2)^{2} - ln x

1/3 [log_{2} x + log_{2} (x - 4)]

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.

Math Worksheets

Videos, worksheets, examples, solutions, and activities to help Algebra students learn how to simplify or combine or condense logarithmic expressions using the properties of logarithm.

The following table gives the Logarithmic Properties. Scroll down the page for more examples and solutions.

How to condense or combine a logarithmic expression into a single logarithm using the properties of logarithms?

Examples:

Combine into a single logarithm.

2log

2log 8 - 3log 2

Examples:

Combine into a single logarithm.

5ln x + 1/2 ln y - 7 ln z

4log 2 - 2log 3 - log 4

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.

Properties of Logs - Simplify Expression

Apply the properties of logarithms to write a single expression.

Examples:

Write as a single expression.

1. log √2 + log

2. ln 33 - ln 3

Examples:

1/2 log

2 ln (x + 2)

1/3 [log

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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