# Algebra II : Solving and Graphing Exponential Equations

## Example Questions

### Example Question #62 : Solving Exponential Equations

Solve for .

Explanation:

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

With the same base, we now can write

Divide  on both sides.

### Example Question #63 : Solving Exponential Equations

Solve for .

Explanation:

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

With the same base, we can now write

Divide  on both sides.

### Example Question #64 : Solving Exponential Equations

Solve for .

Explanation:

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

With the same base, we can now write

Divide  on both sides.

### Example Question #65 : Solving Exponential Equations

Solve for .

Explanation:

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 power rule of exponents.

With the same base, we can now write

Subtract  on both sides.

Divide  on both sides.

### Example Question #66 : Solving Exponential Equations

Solve for .

Explanation:

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.

Divide  on both sides.

### Example Question #67 : Solving Exponential Equations

Solve for .

Explanation:

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.

Divide  on both sides.

### Example Question #68 : Solving Exponential Equations

Solve for .

Explanation:

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.

Add  and subtract  on both sides.

Divide  on both sides.

### Example Question #71 : Solving Exponential Equations

Solve for .

Explanation:

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 .

Explanation:

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

### Example Question #73 : Solving Exponential Equations

Solve the equation:

Explanation:

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.