# SAT II Math II : Solving Exponential, Logarithmic, and Radical Functions

## Example Questions

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

Rewrite as a single logarithmic expression:

Explanation:

Using the properties of logarithms

and ,

simplify as follows:

### Example Question #2 : Solving Exponential, Logarithmic, And Radical Functions

Simplify by rationalizing the denominator:

Explanation:

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 #3 : Solving Exponential, Logarithmic, And Radical Functions

Simplify:

You may assume that  is a nonnegative real number.

Explanation:

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 #3 : Solving Exponential, Logarithmic, And Radical Functions

Let .   What is the value of ?

Explanation:

Replace the integer as .

Evaluate each negative exponent.

Sum the fractions.

Find :