The Product Rule of Logarithms

Properties of Logarithms

By Ryan Meneses

Vocabulary

​Condense- Rewriting logarithms in simplest for (1 term)

Expand​- Rewriting logarithms from 1 term, to multiple terms.

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3 Logarithmic Properties

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1. Product Rule

2. Quotient Rule

3. Power Rule

Product Rule

​log_b(MN) = log_b(M) + log_b(N)

​Example:

​

log₇8 + log₇6 = ?​

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Multiple Choice

$$\log_312\ +\ \log_34\ =?$$  

• $$\log_314$$  

• $$\log_320$$  

• $$\log48$$  

• $$\log_348$$  

Remember!!!

​To use these logarithmic properties, the log bases MUST be the same!

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Quotient Rule

​log_b(M/N) = log_bM - log_bN

Example:

​

log₅20 - log₅4 = ?​

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Multiple Choice

$$\log_342\ -\ \log_36\ =?$$  

• $$\log7$$  

• $$\log6$$  

• $$\log_37$$  

• $$\log_36$$  

Power Rule

​log_bM^p = p ⋅ log_bM

Example:

​

3 ⋅ log₄8 = ?

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Multiple Choice

$$5\cdot\log_72\ =\ ?$$  

• $$\log32$$  

• $$\log_532$$  

• $$\log_{32}5$$  

• $$\log_732$$  

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Multiple Choice

$$3\cdot\log_43-\log_49\ =\ ?$$  

• $$\log_43$$  

• $$\log_49$$  

• $$\log4$$  

• $$\log_427$$  

Multiple Choice

$$\log_65\ +2\cdot\log_64\ =\ ?$$  

• $$\log_625$$  

• $$\log_680$$  

• $$\log_620$$  

• $$\log80$$  

Multiple Choice

$$\log_6\ \frac{4x}{7}$$  

• $$\log_64x$$  

• $$\log_64x+\log_67$$  

• $$\log_64x-\log_67$$  

• $$4x\cdot\log_67$$