##
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 function.

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

**Problem 8.1d:**

**Answer:**
The exact answer is
and the approximate answer is

**Solution:**

Note that the domain of
is the set of positive
real numbers not equal to 1 because the base may not be negative and the
base may not equal 1.

Convert
to an exponential equation with base
2*x*.

The exact value is
and the approximate answer is

Check the solution
by substituting
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
2.10858166325 for x,
then
2.10858166325 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
*x*=2.10858166325. This means that
is
the real solution.

If you have a difficult time graphing the equation
try graphing the equivalent equation

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

**
If you would like to go back to the beginning of this section, click
on Beginning.
**

**
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

For any comments regarding this page, please send an email to

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