## 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.

Problem 4:

Solution:

The above equation is valid only if all of the terms are valid. The first term is valid if x>4, the second term is valid if the third term is valid if and the fourth term is valid if . Therefore, the equation is valid when all four of these conditions are met, or when x>4. The domain is the set of real numbers greater than 4.

Simplify both sides of the equation using the rules of logarithms.

Recall that if then a = b. Therefore, if

Use the Quadratic Formula to solve for x.

Check the answer x=10.163685265 by substituting 10.163685265 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 10.163685265 for x, then x = 10.163685265 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 10.163685265. This means that 10.163685265 is the real solution.

If you would like to go to the next section, click on next.

If you would like to go back to the previous section, click on previous.

This site was built to accommodate the needs of students. The topics and problems are what students ask for. We ask students to help in the editing so that future viewers will access a cleaner site. If you feel that some of the material in this section is ambiguous or needs more clarification, please let us know by e-mail.

[Algebra] [Trigonometry]
[Geometry] [Differential Equations]
[Calculus] [Complex Variables] [Matrix Algebra]

Do you need more help? Please post your question on our S.O.S. Mathematics CyberBoard.

Author: Nancy Marcus