# Algebra II : Solving Exponential Equations

## Example Questions

### Example Question #51 : 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.

With the same base, we can write:

Take the square root on both sides and account for negative as well.

### Example Question #52 : 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. We don't have the same base in this case, but we do know that . Therefore:

Apply power rule of exponents.

With the same base, we can now write:

Take square root on both sides. Remember to account for negative.

### Example Question #3831 : Algebra Ii

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. We don't have the same base in this case, but we do know that

Therefore:

With the same base, we can now write

Subtract  on both sides.

### Example Question #3832 : Algebra Ii

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. We don't have the same base in this case, but we do know that

therefore

With the same base, we can now write:

Subtract  on both sides.

Divide  on both sides.

### Example Question #3833 : Algebra Ii

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. We don't have the same base in this case, but we do know that

and . By choosing base , we will have the same base and set-up an equation.

Apply power rule of exponents.

With the same base, we can now write

Subtract  on both sides.

Divide  on both sides.

### Example Question #3834 : Algebra Ii

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. We don't have the same base in this case, but we do know that

therefore

Apply power rule of exponents.

With the same base, we can now write

Subtract  and add  on both sides.

Divide  on both sides.

### Example Question #3835 : Algebra Ii

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. We don't have the same base in this case, but we do know that

therefore

With the same base, we can now write

Subtract  on both sides.

Divide  on both sides.

### Example Question #3836 : Algebra Ii

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. We don't have the same base in this case, but we do know that

therefore

With the same base, we now have

Subtract  on both sides.

Divide  on both sides.

### Example Question #3837 : Algebra Ii

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. We don't have the same base in this case, but we do know that

By having a base of , this will make solving equations easier.

Apply power rule of exponents.

With the same base, we now can write

Add  and subtract  on both sides.

Divide  on both sides.

### Example Question #3838 : Algebra Ii

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. We don't have the same base in this case, but we do know that

therefore

Apply power rule of exponents.

With the same base,  we can now write

Add  and subtract  on both sides.

Divide  on both sides.