# High School Math : Solving Exponential Equations

## Example Questions

### Example Question #1 : Solving Exponential Equations

Which value for  satisfies the equation ?

Explanation:

is the only choice from those given that satisfies the equation. Substition of  for  gives:

### Example Question #2 : Solving Exponential Equations

Solve for :

Explanation:

To solve for  in the equation

Factor  out of the expression on the left of the equation:

Use the "difference of squares" technique to factor the parenthetical term on the left side of the equation.

Any variable that causes any one of the parenthetical terms to become  will be a valid solution for the equation.  becomes  when  is , and  becomes  when  is , so the solutions are  and .

### Example Question #1 : Solving Exponential Equations

Solve for  (nearest hundredth):

Explanation:

Take the common logarithm of both sides and solve for :

### Example Question #4 : Solving Exponential Equations

Solve for  (nearest hundredth):

Explanation:

, so  can be rewritten as

### Example Question #5 : Solving Exponential Equations

Solve for  (nearest hundredth):

Explanation:

One method: Take the natural logarithm of both sides and solve for :

### Example Question #1 : 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 #1 : 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 #1 : Solving Exponential Equations

What are the x-intercepts of this equation?