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 8.2c:
Answer:
The exact answer is 
and the approximate answer is 
Solution:
Note that the domain of 
is the set of real numbers
such that 5 - 2x > 0, or when 
because you cannot take the
log of zero or a negative number. If any of your answers are greater than or
equal to 
, you must discard them as extraneous solutions.
Let's start the process to find the solution to the equation.
Isolate the logarithmic term.
Convert the logarithmic equation to an exponential equation with base e.
Solve for x by isolating x.
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.
for x, then 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 . This means that is the real solution.
If you would like to review the solution to problem 8.2d, 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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