### All SAT II Math II Resources

## Example Questions

### Example Question #1 : Exponents And Logarithms

To the nearest hundredth, solve for :

**Possible Answers:**

The equation has no solution.

**Correct answer:**

Take the common logarithm of both sides, then solve the resulting linear equation.

### Example Question #1 : Exponents And Logarithms

Solve for :

**Possible Answers:**

**Correct answer:**

Take the common logarithm of both sides:

### Example Question #1 : Exponents And Logarithms

Solve for :

**Possible Answers:**

**Correct answer:**

The base of the common logarithm is 10, so

The sum of three logarithms is the logarithm of the product of the three powers, so:

Therefore,

### Example Question #1 : Exponents And Logarithms

To the nearest hundredth, solve for :

**Possible Answers:**

**Correct answer:**

### Example Question #1 : Exponents And Logarithms

Solve for :

**Possible Answers:**

The equation has no solution

**Correct answer:**

The base of the common logarithm is 10, so

The sum of logarithms is the logarithm of the product of the three powers, and the difference of logarithms is the logarithm of the quotient of their powers. Therefore,

### Example Question #11 : Exponents And Logarithms

Give the set of real solutions to the equation

(round to the nearest hundredth, if applicable)

**Possible Answers:**

The equation has no solution.

**Correct answer:**

Using the Product of Powers Rule, then the Power of a Power Rule, rewrite the first two terms strategically:

Substitute for ; the equation becomes

Factor this as

by finding two integers whose product is 3 and whose sum is . Through some trial and error we find , so we can write

By the Zero Product Rule, one of these two factors must be equal to 0.

If , then .

Substituting back for :

.

If , then .

Substituting back for :

Both can be confirmed to be solutions by substitution.

### Example Question #11 : Exponents And Logarithms

Give the solution set:

**Possible Answers:**

The equation has no solution.

**Correct answer:**

Rewrite by taking advantage of the Product of Powers Property and the Power of a Power Property:

Substitute for ; the resulting equation is the quadratic equation

which can be written in standard form by subtracting from both sides:

The trinomial can be factored by the method, Look for two integers with sum and product ; by trial and error, we find they are , so the equation can be rewritten and solved by grouping:

By the Zero Product Property, one of these factors must be equal to 0.

Either

Substituting back for :

Or:

Substituting back for :

The solution set, as can be confirmed by substituting in the equation, is .

### Example Question #11 : Exponents And Logarithms

Solve for :

**Possible Answers:**

**Correct answer:**

and , so,

can be rewritten as

Applying the Power of a Power Rule,

### Example Question #12 : Exponents And Logarithms

Solve the equation:

**Possible Answers:**

**Correct answer:**

Rewrite the base of the right side.

Simplify the right side.

Add 6 on both sides.

Divide by 6 on both sides.

The answer is:

### Example Question #13 : Exponents And Logarithms

Solve:

**Possible Answers:**

**Correct answer:**

Change the base of the left side to base two.

The equation becomes:

Set the exponents equal since they have similar bases.

Divide by 2 on both sides.

The answer is:

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