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

Study concepts, example questions & explanations for SAT II Math II

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Example Questions

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

Rewrite as a single logarithmic expression:

Possible Answers:

Correct answer:

Explanation:

Using the properties of logarithms

 and ,

simplify as follows:

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

Simplify by rationalizing the denominator:

Possible Answers:

Correct answer:

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.

Possible Answers:

Correct answer:

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 #4 : Solving Exponential, Logarithmic, And Radical Functions

Let .   What is the value of ?

Possible Answers:

Correct answer:

Explanation:

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:

Explanation:

Square both sides to eliminate the radical.

Add five on both sides.

Divide by negative three on both sides.

The answer is:  

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