### All SAT II Math II Resources

## Example Questions

### Example Question #21 : Exponents And Logarithms

Solve

**Possible Answers:**

**Correct answer:**

First, subtract the natural log terms:

Now rewrite the equation in exponential form:

Finally, isolate the variable:

### Example Question #21 : Exponents And Logarithms

Solve

**Possible Answers:**

**Correct answer:**

We can start by canceling the logs, because they both have the same base:

Now we can collect constants on one side of the equation, and variables on the other:

### Example Question #31 : Mathematical Relationships

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 #51 : Sat Subject Test In Math Ii

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 #53 : Sat Subject Test In Math Ii

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 #21 : Exponents And Logarithms

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 #21 : Exponents And Logarithms

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 #22 : 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.