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:
The above equation is valid only if all of the terms are valid. The first
term is valid if x>0, the second term is valid if 
or 
and
the third term is valid if x>0. Therefore, the equation is valid when all
three of these conditions are met, or when 
The domain is the
set of real numbers greater than 
.
Simplify both sides of the equation using the rules of logarithms.
Recall that if 
a = b. Therefore, if
Solve for x.
The exact answer is 4.
Check the answer x = 4 by substituting 4 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.
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 4. This means that 4 is the real
solution.
If you would like to test yourself by working some problems similar to this
example, click on problem.
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