High School Math : Solving Exponential Equations

Study concepts, example questions & explanations for High School Math

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Example Questions

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Example Question #1 : Solving Exponential Equations

Which value for  satisfies the equation ?

 

Possible Answers:

Correct answer:

Explanation:

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

Example Question #2 : Solving Exponential Equations

Solve for :

Possible Answers:

Correct answer:

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):

Possible Answers:

Correct answer:

Explanation:

Take the common logarithm of both sides and solve for :

Example Question #3 : Solving Exponential Equations

Solve for  (nearest hundredth):

Possible Answers:

Correct answer:

Explanation:

, so  can be rewritten as

Example Question #2 : Solving Exponential Equations

Solve for  (nearest hundredth):

Possible Answers:

Correct answer:

Explanation:

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

Example Question #5 : Solving Exponential Equations

Solve for :

Possible Answers:

The equation has no solution.

Correct answer:

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 #6 : Solving Exponential Equations

Solve for :

Possible Answers:

The equation has no solution

Correct answer:

Explanation:

, so we can rewrite the equation as follows:

Example Question #35 : Exponents

What are the y-intercepts of the equation?

Possible Answers:

This equation does not have a y-intercept.

Correct answer:

Explanation:

To find the y-intercepts, set  and solve.

Example Question #7 : Solving Exponential Equations

What are the y-intercepts of the equation?

Possible Answers:

There are no y-intercepts for this equation.

Correct answer:

Explanation:

To find the y-intercepts, set  and solve.

Example Question #3 : Solving Exponential Equations

What are the x-intercepts of this equation?

Possible Answers:

Correct answer:

Explanation:

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

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