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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 1:**

Note that the domain of is the set of real numbers greater than
zero because you cannot take the log of zero or a negative number.

The exact value is and the approximate value

Check the solution by substituting 20.085537 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 20.085537 for x, then
*x*=20.085537 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 20.085537.
This means that 20.085537 is the real solution.

**
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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