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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 8.1c:
**
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**
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**
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** Answer: **
** and the approximate answer is **

**Solution:**

Note that the domain of
is the set
of real numbers such that -2*x*>0 or

Convert
to an exponential
equation with base

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.

Since the left side of the original equation is equal to the right side of
the original equation after we substitute the value
-0.002569115543 for x,
then
-0.002569115543 is a solution.**
**

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**
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**
**

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*=-0.002569115543. This means that
is
the real solution.**
**

**
**

If you have trouble graphing the equation
,
try graphing the equivalent equation
**
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**
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**
If you would like to review the solution to problem 8.1d, click on Solution.
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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**

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**
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