These lessons help Algebra students learn how to simplify or combine or condense logarithmic expressions using the properties of logarithm.

**Related Pages**

Common And Natural Logarithm

Logarithmic Functions

Logarithm Properties

More Lessons for Grade 9

**Combining Logarithmic Expressions**

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

**Example:**

Combine into a single logarithm.

2log5x + 3log52

2log 8 - 3log 2

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

**Example:**

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.

**Example:**

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?**

**Example:**

1/2 log8 x + 3 log8 (x + 1)

2 ln (x + 2)2 - ln x

1/3 [log2 x + log2 (x - 4)]

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