### All SAT II Math I Resources

## Example Questions

### Example Question #1 : Exponents And Logarithms

How many elements are in a set that has exactly 128 subsets?

**Possible Answers:**

None of the other responses is correct.

**Correct answer:**

A set with elements has subsets.

Solve:

### Example Question #1 : Exponents And Logarithms

Rewrite as a single logarithmic expression:

**Possible Answers:**

**Correct answer:**

Using the properties of logarithms

and ,

we simplify as follows:

### Example Question #2 : Exponents And Logarithms

Solve:

**Possible Answers:**

**Correct answer:**

In order to solve this problem, covert 27 to the correct base and power.

Since , the correct answer is .

### Example Question #3 : Exponents And Logarithms

Simplify

**Possible Answers:**

**Correct answer:**

When an exponent is raised by another exponent, we just multiply the powers.

### Example Question #4 : Exponents And Logarithms

Simplify:

**Possible Answers:**

**Correct answer:**

When adding exponents, we don't add the exponents or multiply out the bases. Our goal is to see if we can factor anything. We do see three . Let's factor.

Remember when multiplying exponents, we just add the powers.

### Example Question #1 : Exponents And Logarithms

Solve and simplify.

**Possible Answers:**

**Correct answer:**

Another way to write this is . The only number that makes is .

### Example Question #6 : Exponents And Logarithms

Simplify:

**Possible Answers:**

**Correct answer:**

is the same as . Let's factor out . It's the same as . Therefore which is the answer to our question.

### Example Question #2 : Exponents And Logarithms

Simplify:

**Possible Answers:**

**Correct answer:**

When dealing with subtraction in regards to logarithms, it's the same as dividing the numbers.

### Example Question #8 : Exponents And Logarithms

Simplify:

**Possible Answers:**

**Correct answer:**

When dealing with addition in regards to logarithms, it's the same as multiplying the numbers.

### Example Question #9 : Exponents And Logarithms

Solve: when .

**Possible Answers:**

**Correct answer:**

Power rule says when an exponent is raised to another exponent, you must multiply the exponents.

So and our expression is now .

Plug in the given value to get

.

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