### All Algebra II Resources

## Example Questions

### Example Question #4 : Solving Exponential Equations

Solve for .

**Possible Answers:**

**Correct answer:**

8 and 4 are both powers of 2.

### Example Question #5 : Solving Exponential Equations

Solve for :

**Possible Answers:**

No solution

**Correct answer:**

Because both sides of the equation have the same base, set the terms equal to each other.

Add 9 to both sides:

Then, subtract 2x from both sides:

Finally, divide both sides by 3:

### Example Question #6 : Solving Exponential Equations

Solve for :

**Possible Answers:**

No solution

**Correct answer:**

125 and 25 are both powers of 5.

Therefore, the equation can be rewritten as

.

Using the Distributive Property,

.

Since both sides now have the same base, set the two exponents equal to one another and solve:

Add 30 to both sides:

Add to both sides:

Divide both sides by 20:

### Example Question #7 : Solving Exponential Equations

Solve .

**Possible Answers:**

No solution

**Correct answer:**

Both 27 and 9 are powers of 3, therefore the equation can be rewritten as

.

Using the Distributive Property,

.

Now that both sides have the same base, set the two exponenents equal and solve.

Add 12 to both sides:

Subtract from both sides:

### Example Question #8 : Solving Exponential Equations

**Possible Answers:**

**Correct answer:**

The first step in thist problem is divide both sides by three: . Then, recognize that 8 could be rewritten with a base of 2 as well (). Therefore, your answer is 3.

### Example Question #9 : Solving Exponential Equations

Solve for .

**Possible Answers:**

**Correct answer:**

Let's convert to base .

We know the following:

Simplify.

Solve.

### Example Question #10 : Solving Exponential Equations

Solve for .

**Possible Answers:**

**Correct answer:**

Let's convert to base .

We know the following:

Simplify.

Solve.

.

### Example Question #11 : Solving Exponential Functions

Solve for .

**Possible Answers:**

**Correct answer:**

When multiplying exponents with the same base, we will apply the power rule of exponents:

We will simply add the exponents and keep the base the same.

### Example Question #12 : Solving Exponential Functions

Solve for .

**Possible Answers:**

**Correct answer:**

When multiplying exponents with the same base, we will apply the power rule of exponents:

We will simply add the exponents and keep the base the same.

Simplify.

Solve.

### Example Question #13 : Solving Exponential Functions

Solve for .

**Possible Answers:**

**Correct answer:**

When adding exponents with the same base, we need to see if we can factor out the numbers of the base.

In this case, let's factor out .

We get the following:

Since we are now multiplying with the same base, we get the following expression:

Now we have the same base and we just focus on the exponents.

The equation is now:

Solve.