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 2:**

The above equation is valid only if
or
The domain is the set of real numbers greater than

Simplify the left side of the equation using the rules of logarithms.

Convert the equation to an exponential equation with base 6.

This answer may or may not be the solution to the original equation. You
must check this answer by substitution or by graphing with the original
equation.

**Numerical Check:**

Check the answer *x*=7.75 by substituting 7.75 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 7.75 for x, then *x*=7.75 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 7.75. This means that 7.75 is the real solution. **
**

**
**

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**
**

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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.

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contents.

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