# Algebra II : Solving Exponential Equations

## Example Questions

### 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.

Divide by 9 on both sides.

### Example Question #74 : Solving Exponential Equations

Solve:

Explanation:

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.

### Example Question #75 : Solving Exponential Equations

Solve for .

Explanation:

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 .

Explanation:

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 .

Explanation:

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 .

Explanation:

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.

Divide  on both sides.

### Example Question #79 : Solving Exponential Equations

Solve for .

Explanation:

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 .

Explanation:

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