College Algebra : Logarithmic Functions

Study concepts, example questions & explanations for College Algebra

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Example Questions

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Example Question #10 : Exponential And Logarithmic Functions

Solve the following for x:

Possible Answers:

Correct answer:

Explanation:

To solve, you must first "undo" the log. Since no base is specified, you assume it is 10. Thus, we need to take 10 to both sides.

Now, simply solve for x.

Example Question #1 : Logarithmic Functions

Simplify the following:

Possible Answers:

Correct answer:

Explanation:

To solve, you must combine the logs into 1 log, instead of three separate ones. To do this, you must remember that when adding logs, you multiply their insides, and when you subtract them, you add their insides. Therefore,

Example Question #1 : Logarithmic Functions

Solve for y in the following expression:

Possible Answers:

Correct answer:

Explanation:

To solve for y we first need to get rid of the logs.

Then we get .

After that, we simply have to divide by 5x on both sides:

Example Question #2 : Logarithmic Functions

Solve for .

Possible Answers:

Correct answer:

Explanation:

To solve this natural logarithm equation, we must eliminate the  operation. To do that, we must remember that  is simply  with base . So, we raise both side of the equation to the  power.

This simplifies to

. Remember that anything raised to the 0 power is 1.

Continuing to solve for x,

Example Question #3 : Logarithmic Functions

Solve for .

Possible Answers:

Correct answer:

Explanation:

To eliminate the  operation, simply raise both side of the equation to the  power because the base of the  operation is 7.

This simplifies to 

Example Question #5 : Logarithmic Functions

True or false:

if and only if either  or .

Possible Answers:

False

True

Correct answer:

False

Explanation:

is a direct statement of the Change of Base Property of Logarithms. If  and , this property holds true for any  - not just .

Example Question #6 : Logarithmic Functions

Evaluate 

Possible Answers:

 is an undefined quantity.

Correct answer:

 is an undefined quantity.

Explanation:

 is undefined for two reasons: first, the base of a logarithm cannot be negative, and second, a negative number cannot have a logarithm. 

Example Question #4 : Logarithmic Functions

Use the properties of logarithms to rewrite as a single logarithmic expression:

Possible Answers:

Correct answer:

Explanation:

, so

, so the above becomes

, so the above becomes

Example Question #8 : Logarithmic Functions

Use the properties of logarithms to rewrite as a single logarithmic expression:

Possible Answers:

None of the other choices gives the correct response.

Correct answer:

Explanation:

, so

, so the above becomes

By the Change of Base Property,

, so the above becomes

,

the correct response.

Example Question #9 : Logarithmic Functions

Expand the logarithm: 

Possible Answers:

None of these

Correct answer:

Explanation:

We expand this logarithm based on the property: 

and .

 

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