# Algebra II : Solving and Graphing Exponential Equations

## Example Questions

### 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

Add  on both sides.

Divide  on both sides.

### Example Question #81 : 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

Add  on both sides.

Divide  on both sides.

### Example Question #82 : 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 #81 : Solving And Graphing 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

Apply power rule of exponents.

With the same base, we can now write

Subtract  on both sides.

Divide  on both sides.