SOLVING EXPONENTIAL EQUATIONS

EXPONENTIAL EQUATIONS

Note:

To solve an exponential equation, isolate the exponential term, take the logarithm of both sides and solve.

If you would like an in-depth review of exponents, the rules of exponents, exponential functions and exponential equations, click on exponential function

Solve for the real number x in the following equation.

Problem 7.1d:

Answer:There is no real answer.

Solution:

If you did not make this observation early on, you'd catch it during the process of solving or checking your answer.

Take the natural logarithm of both sides of the equation

eqnarray30

You cannot take the natural logarithm of a negative number and come up with a real number answer.

You can also check your answer by graphing (formed by subtracting the right side of the original equation from the left side). Look to see where the graph crosses the x-axis; that will be the real solution. Note that the graph never crosses the x-axis. This means that there is no real solution.

If you would like to go back to the beginning of this section, click on Beginning.

If you would like to go to the next level of solving exponential equations, click on Next.

If you would like to go back to the equation table of contents, click on Contents.
This site was built to accommodate the needs of students. The topics and problems are what students ask for. We ask students to help in the editing so that future viewers will access a cleaner site. If you feel that some of the material in this section is ambiguous or needs more clarification, please let us know by e-mail.

[Algebra] [Trigonometry] [Geometry] [Differential Equations] S.O.S MATHematics home page

Do you need more help? Please post your question on our S.O.S. Mathematics CyberBoard.

Author: Nancy Marcus