SAT II Math I : Exponents and Logarithms

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

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Example Questions

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Example Question #1 :Mathematical Relationships

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

Possible Answers:

None of the other responses is correct.

Correct answer:

Explanation:

A set withelements hassubsets.

Solve:

Example Question #1 :Exponents And Logarithms

Rewrite as a single logarithmic expression:

Possible Answers:

Correct answer:

Explanation:

Using the properties of logarithms

and,

we simplify as follows:

Example Question #1 :Exponents And Logarithms

Solve:

Possible Answers:

Correct answer:

Explanation:

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

Since, the correct answer is.

Example Question #2 :Exponents And Logarithms

Simplify

Possible Answers:

Correct answer:

Explanation:

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

Example Question #3 :Exponents And Logarithms

Simplify:

Possible Answers:

Correct answer:

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 #2 :Exponents And Logarithms

Solve and simplify.

Possible Answers:

Correct answer:

Explanation:

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

Example Question #1 :Exponents And Logarithms

Simplify:

Possible Answers:

Correct answer:

Explanation:

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

Example Question #4 :Exponents And Logarithms

Simplify:

Possible Answers:

Correct answer:

Explanation:

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

Example Question #5 :Exponents And Logarithms

Simplify:

Possible Answers:

Correct answer:

Explanation:

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

Example Question #1 :Exponents And Logarithms

Solve:when.

Possible Answers:

Correct answer:

Explanation:

Power rule says when an exponent is raised to another exponent, you must multiply the exponents.

Soand our expression is now.

Plug in the given value to get

.

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