Solving Logarithmic Equations Worksheet
ADVERTISEMENT
1
2
3
4
5
6
7
8Solving Logarithmic Equations
Deciding How to Solve Logarithmic Equation
log (5x 7) 5
+
=
log (7x 3) log (5x 9),
+
=
+
When asked to solve a logarithmic equation such as
or
the first
2
3
3
thing we need to decide is how to solve the problem. Some logarithmic problems are solved by simply
dropping the logarithms while others are solved by rewriting the logarithmic problem in exponential form.
How do we decide what is the correct way to solve a logarithmic problem? The key is to look at the problem
and decide if the problem contains only logarithms or if the problem has terms without logarithms.
log (5x 7) 5,
+
=
If we consider the problem
this problem contains a term, 5, that does not have a logarithm.
2
So, the correct way to solve these types of logarithmic problems is to rewrite the logarithmic problem in
log (7x 3) log (5x 9),
+
=
+
exponential form. If we consider the example
this problem contains only
3
3
logarithms. So, the correct way to solve these types of logarithmic problems is to simply drop the
logarithms.
Properties of Logarithms Revisited
When solving logarithmic equation, we may need to use the properties of logarithms to simplify the
problem first. The properties of logarithms are listed below as a reminder.
Properties for Condensing Logarithms
Property 1:
0 log 1
=
– ZeroExponent Rule
a
Property 2:
1 log a
=
a
Property 3:
log x log y log (xy)
+
=
– Product Rule
a
a
a
æ ö
x
Property 4:
log x log y log
-
=
– Quotient Rule
ç ÷
a
a
a
y
è ø
y
Property 5:
– Power Rule
y log x
=
log x
a
a
Solving Logarithmic Equations Containing Only Logarithms
After observing that the logarithmic equation contains only logarithms, what is the next step?
OneToOne Property of Logarithms
If
log M log N,
=
then M = N.
b
b
This statement says that if an equation contains only two logarithms, on opposite sides of the equal sign,
with the same base then the problem can be solved by simply dropping the logarithms.
ADVERTISEMENT
0 votes
Related Articles
Related forms
Related Categories
Parent category: Education