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 2:
The above equation is valid only if all of the terms are valid. The first
term is valid if 3x- 5 > 0 or 
the second term is valid if
2x- 3 > 0 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 
then a=b . Therefore, if
Solve for x.
The exact answer is 
and the approximate answer is
Check the answer 
by substituting 8.63104367407
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 8.63104367407. This means that 8.63104367407 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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