# Precalculus : Properties of Logarithms

## Example Questions

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### Example Question #61 : Properties Of Logarithms

Expand this logarithm: Possible Answers:

None of the other answers.    Correct answer: Explanation: Use the Quotient property of Logarithms to express on a single line: Use the Product property of Logarithms to expand the two terms further: Finally use the Power property of Logarithms to remove all exponents: The expression is now fully expanded.

### Example Question #62 : Properties Of Logarithms

Expand the following logarithm: Possible Answers:    Correct answer: Explanation:

Expand the following logarithm: To expand this log, we need to keep in mind 3 rules:

1) When dividing within a , we need to subtract

2) When multiplying within a , we need to add

3) When raising to a power within a , we need to multiply by that number

These will make more sense once we start applying them.

First, let's use rule number 1 Next, rule 2 sounds good. Finally, use rule 3 to finish up! Making our answer ### Example Question #63 : Properties Of Logarithms

Completely expand this logarithm: Possible Answers:     Correct answer: Explanation: Quotient property: Product property: Power property: ### Example Question #64 : Properties Of Logarithms

Fully expand: Possible Answers:     Correct answer: Explanation:

In order to expand the expression, use the log rules of multiplication and division.  Anytime a variable is multiplied, the log is added.  If the variable is being divided, subtract instead. When there is a power to a variable when it is inside the log, it can be pulled down in front of the log as a coefficient. The answer is: ### Example Question #65 : Properties Of Logarithms

Expand the following: Possible Answers:    Correct answer: Explanation:

To solve, simply remember that when you add logs, you multiply their insides.

Thus, ### Example Question #66 : Properties Of Logarithms

Express the following in expanded form. Possible Answers:    Correct answer: Explanation:

To solve, simply remember that when adding logs, you multiply their insides and when subtract logs, you divide your insides. You must use this in reverse to solve. Thus, ### Example Question #67 : Properties Of Logarithms

Completely expand this logarithm: Possible Answers:    The answer is not present.

Correct answer: Explanation:

We expand logarithms using the same rules that we use to condense them.

Here we will use the quotient property and the power property  Use the quotient property: Rewrite the radical: Now use the power property: ### Example Question #68 : Properties Of Logarithms

Expand the logarithm Possible Answers:    Correct answer: Explanation:

In order to expand the logarithmic expression, we use the following properties

• • As such ### Example Question #69 : Properties Of Logarithms

Given the equation , what is the value of ? Use the inverse property to aid in solving.

Possible Answers:     Correct answer: Explanation:

The natural logarithm and natural exponent are inverses of each other.  Taking the of will simply result in the argument of the exponent.

That is Now, , so 1 2 3 4 5 7 Next →

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