## SOLVING 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 x in the following equation.

Example 1:

The first objective is to isolate the expression .

Subtract 5 from both sides of the equation.

Take the natural logarithm of both sides of the equation .

Use the Quadratic Formula where a=1, b=-6, .

and

The exact answers are and the approximate answers are and

Check these answers in the original equation.

Check the solution by substituting 5.88954754282 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.

• Left Side:

• Right Side:

Since the left side of the original equation is equal to the right side of the original equation after we substitute the value 5.88954754282 for x, then x=5.88954754282 is a solution.

Check the solution by substituting 0.110452457185 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.

• Left Side:

• Right Side:

Since the left side of the original equation is equal to the right side of the original equation after we substitute the value 0.110452457185 for x, then x=0.110452457185 is a solution.

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 crosses the x-axis at 5.88954754282 and 0.110452457185. This means that 5.88954754282 and 0.110452457185 are the real solutions.

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 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]

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

Author: Nancy Marcus

Copyright © 1999-2019 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