SAT II Math I : Exponents and Logarithms

Example Questions

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Example Question #1 : Exponents And Logarithms

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

None of the other responses is correct.

Explanation:

A set with  elements has  subsets.

Solve:

Example Question #2 : Exponents And Logarithms

Rewrite as a single logarithmic expression:

Explanation:

Using the properties of logarithms

and ,

we simplify as follows:

Example Question #3 : Exponents And Logarithms

Solve:

Explanation:

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

Since , the correct answer is .

Example Question #4 : Exponents And Logarithms

Simplify

Explanation:

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

Example Question #5 : Exponents And Logarithms

Simplify:

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 #6 : Exponents And Logarithms

Solve and simplify.

Explanation:

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

Example Question #7 : Exponents And Logarithms

Simplify:

Explanation:

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

Example Question #8 : Exponents And Logarithms

Simplify:

Explanation:

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

Example Question #9 : Exponents And Logarithms

Simplify:

Explanation:

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

Example Question #10 : Exponents And Logarithms

Solve:  when .

Explanation:

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

So  and our expression is now .

Plug in the given value to get

.

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