##
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.
under Algebra.

**Solve for x in the following equation.**

Example 1:

Isolate the exponential term.

Take the natural logarithm of both sides of the equation

The exact answer is and the approximate answer is

When solving the above problem, you could have used any logarithm. For
example, let's solve it using the logarithmic with base 5.

Check this answer in the original equation.

Check the solution by substituting 4.00733318523 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 4.00733318523 for x,
then *x*=4.00733318523 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 4.00733318523. This
means that 4.00733318523 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 onProblem.

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 © 1999-2015 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