# Simplifying (or Condensing) Logarithmic Expressions

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

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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