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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.**

**Example 5:**

Note that the domain of
is the set of real
numbers greater than zero and not equal to 1 because of the base
restrictions on logarithmic functions.

The exact value is
and the approximate value is
1.19623119885.

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
1.19623119885 for x,
then
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
1.19623119885. This means that
1.19623119885 is the real
solution.

If you have trouble graphing
convert it to the equivalent equation

**
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.

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