### All High School Math Resources

## Example Questions

### Example Question #1 : Logarithmic Functions

You are given that and .

Which of the following is equal to ?

**Possible Answers:**

**Correct answer:**

Since and , it follows that and

### Example Question #1 : Exponential And Logarithmic Functions

**Possible Answers:**

**Correct answer:**

### Example Question #2 : Exponential And Logarithmic Functions

What is ?

**Possible Answers:**

**Correct answer:**

Recall that by definition a logarithm is the inverse of the exponential function. Thus, our logarithm corresponds to the value of in the equation:

.

We know that and thus our answer is .

### Example Question #1 : Properties Of Logarithms

Solve for :

**Possible Answers:**

The correct solution set is not included among the other choices.

**Correct answer:**

The correct solution set is not included among the other choices.

FOIL:

These are our *possible* solutions. However, we need to test them.

:

The equation becomes . This is true, so is a solution.

:

However, negative numbers do not have logarithms, so this equation is meaningless. is not a solution, and is the one and only solution. Since this is not one of our choices, the correct response is "The correct solution set is not included among the other choices."

### Example Question #3 : Exponential And Logarithmic Functions

**Possible Answers:**

**Correct answer:**