### All SAT II Math II Resources

## Example Questions

### Example Question #1 : Solving Exponential, Logarithmic, And Radical Functions

Rewrite as a single logarithmic expression:

**Possible Answers:**

**Correct answer:**

Using the properties of logarithms

and ,

simplify as follows:

### Example Question #1 : Solving Exponential, Logarithmic, And Radical Functions

Simplify by rationalizing the denominator:

**Possible Answers:**

**Correct answer:**

Multiply the numerator and the denominator by the conjugate of the denominator, which is . Then take advantage of the distributive properties and the difference of squares pattern:

### Example Question #1 : Solving Exponential, Logarithmic, And Radical Functions

Simplify:

You may assume that is a nonnegative real number.

**Possible Answers:**

**Correct answer:**

The best way to simplify a radical within a radical is to rewrite each root as a fractional exponent, then convert back.

First, rewrite the roots as exponents.

Then convert back to a radical and rationalizing the denominator:

### Example Question #1 : Solving Exponential, Logarithmic, And Radical Functions

Let . What is the value of ?

**Possible Answers:**

**Correct answer:**

Replace the integer as .

Evaluate each negative exponent.

Sum the fractions.

The answer is:

### Example Question #5 : Solving Exponential, Logarithmic, And Radical Functions

Find :

**Possible Answers:**

**Correct answer:**

Square both sides to eliminate the radical.

Add five on both sides.

Divide by negative three on both sides.

The answer is: