# Algebra II : Solving and Graphing Exponential Equations

## Example Questions

### 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.

### Example Question #3839 : 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.

With the same base, we can now write

Add  and subtract  on both sides.

### Example Question #3840 : 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.

With the same base, we can now write

Take the square root on both sides. Account for negative answer.

### Example Question #61 : 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