SOLVING EXPONENTIAL EQUATIONS


Note:

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 x in the following equation.


Example 5: tex2html_wrap_inline155 tex2html_wrap_inline98


In order to solve this equation, we have to isolate the exponential term. Since we cannot easily do this in the equation's present form, let's tinker with the equation until we have it in a form we can solve.


We cannot easily factor this problem. Therefore, let's see if we can use the Quadratic Formula to solve the problem even thought the equation does not look like a quadratic equation. In fact, it is a quadratic equation in tex2html_wrap_inline100


Let's rewrite the equation tex2html_wrap_inline102 with the following substitutions: tex2html_wrap_inline104 and tex2html_wrap_inline106


eqnarray36



Now you should recognize this as a quadratic equation in t where a=2, b=5, and c=6.


eqnarray43


eqnarray51



No real solutions.


You can also check your answer by graphing tex2html_wrap_inline116 (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 are no real solutions








If you would like to test yourself by working some problems similar to this example, click on Problem


If you would like to go to the next section, 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]
[Calculus] [Complex Variables] [Matrix Algebra]

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

Copyright 1999-2017 MathMedics, LLC. All rights reserved.
Contact us
Math Medics, LLC. - P.O. Box 12395 - El Paso TX 79913 - USA
users online during the last hour