##
SOLVING LOGARITHMIC EQUATIONS

Note:

If you would like an in-depth review of logarithms, the rules of logarithms,
logarithmic functions and logarithmic equations, click on
logarithmic functions.

Solve for x in the following equation.

**
Problem 8.6d:**

**Answers:**T
he exact answers are
The approximate answers are
and

**Solution:**

The above equation is valid only if
is valid. The term
is valid if
or
Therefore, the equation is valid when the
domain is the set of real numbers less than
or
greater than

Covert the logarithmic equation to an exponential equation with base *e*.

The exact answers are
The approximate answers are
and
-0.979582.

These answers may or may not be the solutions to the original equation. You
must check them in the original equation, either by numerical substitution
or by graphing.

**Numerical Check:**

Check the answer
by substituting 2.729582 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 2.729582 for x, then
*x*=2.729582 is a solution.
Check the answer
by substituting -0.979582 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 -0.979582 for x, then
*x*=-0.979582 is a solution.

**Graphical Check:**

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 2.729582 and -0.979582. This means that 2.729582 and -0.979582 are the real solutions.
If you have trouble graphing the above problem, you might try graphing the
equivalent function

**
If you would like to go to the next section, click on
next.
**

If you would like to go back to the previous section, click on
previous.

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,
or you find a mistake, 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