Solving Logarithmic Equations Worksheet Page 2
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8Let’s finish solving the problem
log (7x 3) log (5x 9).
+
=
+
3
3
Since the problem has only two logarithms on opposite
log (7x 3) log (5x 9).
+
=
+
3
3
sides of the equal sign, the problem can be solved by
dropping the logarithms.
7x 3 5x 9
+ =
+
Drop the logarithms.
Finish solving by subtracting 5x from each side, subtracting
x 3
=
3 from each side, and finally dividing each side by 2.
x 3
=
Check the answer; this is an acceptable answer because we
get a positive number when it is plugged back in.
Therefore, the solution to the problem
log (7x 3) log (5x 9)
+
=
+ is x = 3.
3
3
Here is another example, solve
log (x 2) log (x 3) log 14.
-
+
+
=
7
7
7
This problem can be simplified by using Property 3 which
log ((x 2)(x 3)) log 14
-
+
=
7
7
changes the addition of logarithms to multiplication.
Drop the logarithms.
(x 2)(x 3) 14
-
+
=
Simplify the problem by distributing or FOILing and
2
x
- - =
x 6 14
combining like terms.
Solve the problem by subtracting 14 from each to get it
2
x
- -
x 20 0
=
equal to zero, and then factoring or using the quadratic
(x 4)(x 5) 0
+
-
=
formula to find the values of x.
x
= -
4 or x 5
=
x 5
=
Check the answers, only one answer is acceptable because
the other answer produces a negative number when it is
plugged back in.
Therefore, the solution to the problem
log (x 2) log (x 3) log 14
-
+
+
=
is x = 5.
7
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Now that we have looked at a couple of examples of solving logarithmic equations containing only
logarithms, let’s list the steps for solving logarithmic equations containing only logarithms.
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