# High School Math : Solving and Graphing Exponential Equations

## Example Questions

### Example Question #6 : Solving Exponential Equations

Solve for :

The equation has no solution.

The equation has no solution.

Explanation:

Since , we can rewrite this equation by subsituting and applying the power rule:

This statement is identically false, which means that the original equation is identically false. There is no solution.

### Example Question #7 : Solving Exponential Equations

Solve for :

The equation has no solution

Explanation:

, so we can rewrite the equation as follows:

### Example Question #8 : Solving Exponential Equations

What are the y-intercepts of the equation?

This equation does not have a y-intercept.

Explanation:

To find the y-intercepts, set  and solve.

### Example Question #9 : Solving Exponential Equations

What are the y-intercepts of the equation?

There are no y-intercepts for this equation.

Explanation:

To find the y-intercepts, set  and solve.

### Example Question #10 : Solving Exponential Equations

What are the x-intercepts of this equation?

Explanation:

To find the x-intercepts, set the numerator equal to zero.

### Example Question #11 : Solving Exponential Equations

What are the x-intercepts of the equation?

Explanation:

To find the x-intercepts, set the numerator equal to zero and solve.

We can simplify from here:

Now we need to rationalize. Because we have a square root on the bottom, we need to get rid of it. Since , we can multiply  to get rid of the radical in the denominator.

Since we took a square root, remember that our answer can be either positive or negative, as a positive squared is positive and a negative squared is also positive.

### Example Question #12 : Solving Exponential Equations

What are the y-intercepts of this equation?

There are no y-intercepts.

Explanation:

To find the y-intercept, set  and solve.

### Example Question #13 : Solving Exponential Equations

What are the y-intercepts of this equation?

There are no y-intercepts for the equation.

Explanation:

To find the y-intercept, set  and solve.

### Example Question #14 : Solving Exponential Equations

What are the x-intercepts of the equation?

There are no horizontal asymptotes.

Explanation:

To find the x-intercepts, we set the numerator equal to zero and solve.

However, the square root of a number can be both positive and negative.

Therefore the roots will be

### Example Question #15 : Solving Exponential Equations

What are the x-intercepts of the equation?