SOLVING LOGARITHMIC EQUATIONS
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 3:
Note that the domain of 
is the set of real numbers such that
x-8>0 or x>8 because you cannot take the log of zero or a negative number
Isolate the logarithmic term.
Convert the logarithmic equation to an exponential equation..
The exact answer is 
and the approximate answer 
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.
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 10.3009758909. This means that 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 to the next section, click on Next
If you would like to go back to the previous section, click on Previous
If you would like to go back to the equation table of contents, click on
Contents
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.
Do you need more help? Please post your question on our
S.O.S. Mathematics CyberBoard.
