SOLVING LOGARITHMIC EQUATIONS
SOLVING LOGARITHMIC EQUATIONS
If you would like an in-depth review of exponents, the rules of logarithms,
logarithmic functions and logarithmic equations, click on
logarithmic function.
Note:
Solve for x in the following equation.
Problem 2:
Answer:
4
Solution:
The above equation is valid only if all of the terms are valid. The first
term is valid if 
the second term
is valid if 
and the third term is valid if 
Therefore, the equation is valid when all three
of these conditions are met, or when x > 3. The domain is the set of real
numbers greater than 3.
Simplify both sides of the equation using the rules of logarithms.
Recall that if 
then a = b. Therefore, if
Solve for x.
The exact answers are x = 4 and 
However, only x = 4 is in the
domain.
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 review the solution to problem 8.3c, click on problem.
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