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 8.2a:
Answer:
The exact answer is 
and the approximate answer is 
Solution:
Note that the domain 
is the set of real numbers such
that 4x>0 because you cannot take the log of zero or a negative number.
Isolate the logarithmic term.
Convert the logarithmic equation to an exponential equation of base e.
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
745.23949676. This means that is the real solution.
If you would like to review the solution to 8.2b, click on Solution
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