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 8.2b:
Answer:
The exact answer is 
or 
and the approximate answer is 
Solution:
Note that the domain of 
is the set of real numbers
such that 
or when x>0, because you cannot take the
log of zero or a negative number.
Isolate the logarithmic term.
The exact answer is 
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 1.04004191153. This means that is the
real solutions.
If you have trouble graphing the equation 
try graphing the equivalent equation 
If you would like to review the solution to problem 8.2c, click on
Solution
If you would like to test yourself by working some problems similar to this
example, click on Problem
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