## 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 8.2a:

Solution:

Note that the domain is the set of real numbers such that 4x>0 because you cannot take the log of zero or a negative number.

Isolate the logarithmic term.

Convert the logarithmic equation to an exponential equation of base e.

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 745.23949676 for x, then 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 745.23949676. This means that is the real solution.

If you would like to review the solution to 8.2b, click on Solution

If you would like to go back to the beginning of this section, click on Beginning

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