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.
Problem 8.2d:
Answer: 
The exact answer is 
and the approximate answer is 
Solution:
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.
Isolate the logarithmic term.
Convert the logarithmic equation to an exponential equation.
The exact answers are 
and the approximate
answer is
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 1.06045347096. This means that is
the real solution.
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