# Algebra II : Multiplying and Dividing Logarithms

## Example Questions

### Example Question #1 : Multiplying And Dividing Logarithms

Rewrite the following logarithmic expression in expanded form (i.e. as a sum and/or difference): Possible Answers:     Correct answer: Explanation:

By logarithmic properties: ;  Combining these three terms gives the correct answer: ### Example Question #1 : Simplifying Logarithms

Which of the following is equivalent to Possible Answers:     Correct answer: Explanation:

Recall that log implies base if not indicated.Then, we break up . Thus, we have .

Our log rules indicate that .

So we are really interested in, .

Since we are interested in log base , we can solve without a calculator.

We know that , and thus by the definition of log we have that .

Therefore, we have ### Example Question #3 : Multiplying And Dividing Logarithms

Find the value of the Logarithmic Expression. Possible Answers:     Correct answer: Explanation:

Use the change of base formula to solve this equation.     ### Example Question #4 : Multiplying And Dividing Logarithms

What is another way of expressing the following? Possible Answers:     Correct answer: Explanation:

Use the rule  ### Example Question #5 : Multiplying And Dividing Logarithms

Expand this logarithm: Possible Answers:     Correct answer: Explanation:

In order to solve this problem you must understand the product property of logarithms and the power property of logarithms . Note that these apply to logs of all bases not just base 10. log of multiple terms is the log of each individual one: now use the power property to move the exponent over: ### Example Question #6 : Multiplying And Dividing Logarithms

Which of the following is equivalent to ?

Possible Answers:     Correct answer: Explanation:

We can rewrite the terms of the inner quantity.  Change the negative exponent into a fraction.  This means that: Split up these logarithms by addition. According to the log rules, the powers can be transferred in front of the logs as coefficients.

The answer is: ### Example Question #7 : Multiplying And Dividing Logarithms

Many textbooks use the following convention for logarithms:   Solve: Possible Answers:     Correct answer: Explanation:

Remembering the rules for logarithms, we know that .

This tells us that .

This becomes , which is .

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