Remember that the composition of a function and
its inverse returns the starting value.
A
logarithmic
equation
can be solved using the
properties of
logarithms along with
the use of a common base.
Properties
of Logs:
To solve most
logarithmic equations:
1. Isolate the
logarithmic expression.
(you may need to use the properties
to create one logarithmic term)
2. Rewrite in exponential form
(with a common base)
3. Solve for the variable.
Things to remember
about logs:
Do you see composition of a function and its
inverse at work in the last statements?
Find out more about
exponential and log
functions.
Examples:
Solve for x:
Answer:
1.
ANSWER:
• Isolate the log
expression
• Choose base 10 to correspond with log
(base 10)
• Apply composition of inverses and
solve.
2.
ANSWER:
• Remember that exand ln x are inverse functions.
3.
ANSWER:
4.
ANSWER:
• Isolate the logarithmic
expression first.
5.
ANSWER:
• Use the log property
to express the two
terms on the left as a single term.
•
Remember that log of a negative value is not
a real number and is not considered a
solution.
6.
ANSWER:
7.
Using
your graphing calculator, solve for x to the
nearest hundredth.
Method 2:
Place the left side of the equation into Y1
and the right side into Y2.
Under the CALC menu, use #5 Intersect to
find where the two graphs intersect.
ANSWER: Method 1:
Rewrite so the equation equals zero.
Find the zeros of the function.
Both values are solutions, since both values allow
for the ln of a positive value.
How
to use your
TI-83+/84+ graphing
calculator with
logarithms. Click calculator.
