# SAT II Math I : Exponents and Logarithms

## Example Questions

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### Example Question #1 : Mathematical Relationships

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

None of the other responses is correct.

Explanation:

A set with  elements has  subsets.

Solve:

### Example Question #2 : Exponents And Logarithms

Rewrite as a single logarithmic expression:

Explanation:

Using the properties of logarithms

and ,

we simplify as follows:

### Example Question #1 : Exponents And Logarithms

Solve:

Explanation:

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

Since , the correct answer is .

### Example Question #1 : Exponents And Logarithms

Simplify

Explanation:

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

### Example Question #1 : Exponents And Logarithms

Simplify:

Explanation:

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.

Explanation:

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

### Example Question #7 : Exponents And Logarithms

Simplify:

Explanation:

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

### Example Question #1 : Exponents And Logarithms

Simplify:

Explanation:

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

### Example Question #9 : Exponents And Logarithms

Simplify:

Explanation:

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

Solve:  when .