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 4:**

The above equation is valid only if
Either *x*-8>0 and
or *x*-8<0 and
The domain is
the set of real numbers less than -2 or greater than 8.

Convert the equation to an exponential equation with base 4.

The exact answers are and the approximate answers are 8.0131514 and -2.0131514.

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

**
Numerical Check:**

Check the answer by substituting 8.0131514 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 8.0131514 for x, then
*x*=8.0131514 is a solution.

Check the answer
by substituting
-2.0131514 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
-2.0131514 for x, then
*x*=-2.0131514 is a solution.

**Graphical Check:**

You can also check your answer by graphing

If you are graphing with your calculator you might have a problem with log
base
.
Therefore, convert it to either base e or base 10 to
graph. Most graphing calculators have these functions.

**
If you would like to test yourself by working some problems similar to this
example, click on problem.
**

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