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

## Example Questions

### Example Question #4 : Solving Functions

Rewrite as a single logarithmic expression:       Explanation:

Using the properties of logarithms and ,

simplify as follows:    ### Example Question #5 : Solving 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 #6 : Solving 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 #7 : Solving Functions

Let .   What is the value of ?      Explanation:

Replace the integer as . Evaluate each negative exponent.  Sum the fractions. The answer is: ### Example Question #8 : Solving Functions

Find :       Explanation:

Square both sides to eliminate the radical.     The answer is:  