### All Algebra II Resources

## Example Questions

### Example Question #71 : Solving Exponential Equations

Solve for .

**Possible Answers:**

**Correct answer:**

When solving exponential equations, we need to ensure that we have the same base. When that happens, our equations our based on the exponents. However, since the base is different, we can definitely convert one of the numbers to have the same base. We know that

therefore

Apply the power rule of exponents.

With the same base, we can now write

Add and subtract on both sides.

### Example Question #72 : Solving Exponential Equations

Solve for .

**Possible Answers:**

**Correct answer:**

When solving exponential equations, we need to ensure that we have the same base. When that happens, our equations our based on the exponents. However, since the base is different, we can definitely convert one of the numbers to have the same base. We know that

therefore

Apply the power rule of exponents.

With the same base, we can now write

Add on both sides.

### Example Question #73 : Solving Exponential Equations

Solve the equation:

**Possible Answers:**

**Correct answer:**

Solve by first changing the base of the right side.

Rewrite the equation.

With common bases, we can set the powers equal to each other.

Use distribution to simplify the right side.

Add on both sides.

Add two on both sides.

Divide by 9 on both sides.

The answer is:

### Example Question #74 : Solving Exponential Equations

Solve:

**Possible Answers:**

**Correct answer:**

In order to solve this equation, we will need to change the base of one half to two. Use a negative exponent to rewrite this term.

Rewrite the equation.

Since the bases are common, we can simply set the exponents equal to each other.

Solve for x. Divide a negative one on both sides to eliminate the negatives.

The equation becomes:

Subtract from both sides.

Divide both sides by negative four.

The answer is:

### Example Question #75 : Solving Exponential Equations

Solve for .

**Possible Answers:**

**Correct answer:**

When dealing with exponential equations, we want to make sure the bases are the same. This way we can set-up an equation with the exponents.

With the same base, we can now write

Subtract on both sides.

### Example Question #76 : Solving Exponential Equations

Solve for .

**Possible Answers:**

**Correct answer:**

When dealing with exponential equations, we want to make sure the bases are the same. This way we can set-up an equation with the exponents.

With the same base, we can now write

Subtract on both sides.

### Example Question #77 : Solving Exponential Equations

Solve for .

**Possible Answers:**

**Correct answer:**

When dealing with exponential equations, we want to make sure the bases are the same. This way we can set-up an equation with the exponents.

With the same base, we can now write

Subtract on both sides.

### Example Question #78 : Solving Exponential Equations

Solve for .

**Possible Answers:**

**Correct answer:**

With the same base, we can now write

Subtract on both sides.

Divide on both sides.

### Example Question #79 : Solving Exponential Equations

Solve for .

**Possible Answers:**

**Correct answer:**

When dealing with exponential equations, we want to make sure the bases are the same. This way we can set-up an equation with the exponents. Since the bases are now different, we need to convert so we have the same base. We do know that

therefore

With the same base, we can now write

Subtract on both sides.

Divide on both sides.

### Example Question #80 : Solving Exponential Equations

Solve for .

**Possible Answers:**

**Correct answer:**

When dealing with exponential equations, we want to make sure the bases are the same. This way we can set-up an equation with the exponents. Since the bases are now different, we need to convert so we have the same base. We do know that

therefore

With the same base, we can now write

Add on both sides.

Divide on both sides.

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