### All SAT II Math II Resources

## Example Questions

### Example Question #23 : Exponents And Logarithms

Solve .

**Possible Answers:**

**Correct answer:**

We can start by gathering all the constants to one side of the equation:

Next, we can multiply by to change the signs:

Now we can rewrite the equation in exponential form:

And finally, we can solve algebraically:

### Example Question #24 : Exponents And Logarithms

Solve for :

**Possible Answers:**

**Correct answer:**

In order to solve this problem, rewrite both sides of the equation in terms of raising to an exponent.

Since, , we can write the following:

Since , we can write the following:

Now, we can solve for with the following equation:

### Example Question #31 : Mathematical Relationships

Solve

**Possible Answers:**

No solutions

**Correct answer:**

No solutions

The first thing we need to do is find a common base. However, because one of the bases has an in it (an irrational number), and the other does not, it's going to be impossible to find a common base. Therefore, the question has no solution.

### Example Question #61 : Sat Subject Test In Math Ii

Solve

**Possible Answers:**

No solutions

**Correct answer:**

First, we can simplify by canceling the logs, because their bases are the same:

Now we collect all the terms to one side of the equation:

Factoring the expression gives:

So our answers are:

### Example Question #62 : Sat Subject Test In Math Ii

Solve .

**Possible Answers:**

No solutions

**Correct answer:**

Here, we can see that changing base isn't going to help. However, if we remember that and number raised to the th power equals , our solution becomes very easy.

### Example Question #21 : Exponents And Logarithms

To the nearest hundredth, solve for : .

**Possible Answers:**

None of these

**Correct answer:**

None of these

Take the natural logarithm of both sides:

By the Logarithm of a Power Rule the above becomes

Solve for :

.

This is not among the choices given.

### Example Question #64 : Sat Subject Test In Math Ii

Define .

Evaluate .

**Possible Answers:**

**Correct answer:**

### Example Question #1 : Absolute Value

Define .

Order from least to greatest:

**Possible Answers:**

**Correct answer:**

, or, equivalently,

From least to greatest, the values are

### Example Question #61 : Sat Subject Test In Math Ii

Define an operation as follows:

For all real numbers ,

Evaluate .

**Possible Answers:**

Undefined.

**Correct answer:**

### Example Question #67 : Sat Subject Test In Math Ii

Define an operation as follows:

For all real numbers ,

If , which is a possible value of ?

**Possible Answers:**

**Correct answer:**

, so

can be rewritten as

Therefore, either or . The correct choice is .

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