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 1:**

The above equation is valid only if
or
The domain is the set of real numbers not equal to

Convert the equation to an exponential equation with base 4.

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
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 for x, then is a solution.

Check the answer *x*=-339 by substituting -339 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 -339 for x, then
*x*=-339 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
343.6666666667 and -339. This means that
343.6666666667 and -339 are the real solutions.**
**

**
**

**
**

You may have to change the original equation somewhat to graph it because
most graphing calculators only have the natural log function and the common
log function. Rewrite the original equation
in the equivalent form
and graph it**
**

**
**

**
**

Recall that is equivalent to only for those values of Why is that? The domain of is the set of real numbers , and the domain of is the set of real numbers

**
If you would like to work another example, click on example.
**

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example, click on problem.

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