Precalculus : Properties of Logarithms

Study concepts, example questions & explanations for Precalculus

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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

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