# College Algebra : Logarithmic Functions

## Example Questions

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### Example Question #1 : 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 #2 : 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 #3 : 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 #4 : 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 #5 : 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 #6 : Logarithmic Functions

True or false:

if and only if either  or .

Possible Answers:

True

False

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 #7 : 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 #8 : 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 #9 : 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 #10 : 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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