### All College Algebra Resources

## Example Questions

### Example Question #1 : Logarithmic Functions

Solve the following for x:

**Possible Answers:**

**Correct answer:**

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:**

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:**

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:**

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:**

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

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.

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:**

, 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:**

, 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:**

We expand this logarithm based on the property:

and .