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 4:
Note that the domain of 
is the set of real
numbers such that 
or when 
because you cannot take the log of zero or a negative number. Note that
the expression 
is always positive except at 
Isolate the logarithmic term.
The exact answers are 
and the approximate answers
are 
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.
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 12.5427684616 and -7.54276846159. This means that and -7.54276846159 are the real solutions.
If you have solved the problem by rewriting 
as 
, you would have lost one of the solutions.
If you would like to test yourself by working some problems similar to this
example, click on Problem
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