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 2: tex2html_wrap_inline155tex2html_wrap_inline108

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.

Factor the left side of the equation tex2html_wrap_inline110


The only way that a product can equal zero is if at least one of the factors is zero.


This is impossible. Therefore, tex2html_wrap_inline112 If you did not make this observation, you would have caught it when you tried to take the natural logarithm of both sides since you cannot take the logarithm of a negative number.

Now let's look at the second factor,


Now we have a second equation where the exponential term is isolated. Take the natural logarithm of both sides of the equation tex2html_wrap_inline114


The exact answer is tex2html_wrap_inline116 and the approximate answer is x=1.09861228867.

Check this answer in the original equation.

Check the solution tex2html_wrap_inline116 by substituting 1.09861228867 in the original equation for x. If the left side of the equation equals the right side of the equation after the substitution, you have found the correct answer.

Since the left side of the original equation is equal to the right side of the original equation after we substitute the value 1.09861228867 for x, then x=1.09861228867 is a solution.

You can also check your answer by graphing tex2html_wrap_inline134 (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 crosses the x-axis at one place: 1.09861228867. This means that 1.09861228867 is the real solution.

If you would like to work another example, click on Example

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

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 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 1999-2018 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