A Tutorial on Logarithms
Chapter 8 Section 8.5
• Have your notes and text open to
logarithms for reference.
• Have pencil and paper ready.
• Write down questions you wish to
ask your teacher.
Logarithm Rules
These rules are important. You need to master them
before you try to solve logarithmic equations. Apply them to
the problems on the next 5 slides to see if you understand.
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ln A.B = ln A + ln B
loga x.y = loga x + loga y
ln x/y = ln x - ln y
loga x/y = loga x - loga y
ln xb = b.ln x
loga xb = b.loga x
Have your paper and pencil
ready! Feel free to THINK!!!!
Read directions carefully then solve the problem. Write out each step
on your paper. As you complete a step, click on the
to see the
correct response. If yours is correct, move on to the next step. If yours
is not correct, read the explanation. Condense the following expression.
ln 5 – ln 9 + 2 ln 3
ln 5 – ln 9 + ln 32
ln (5/9) + ln 32
ln
(5/
9
) . (9)
The 2 in front of the ln is the exponent for 3.
Write it as an exponent. Example: 3 ln 5 is ln 53 .
Once exponents are taken care of, apply properties
from left to right. ln A – ln B is equivalent to ln (A/B)
The next property is +. ln C + ln D is
equivalent to ln C . D …also 3 squared is 9.
The final step is simple arithmetic.
ln 5
5/
9
. 9 is 5
Read directions carefully then solve the problem. Write out each step
on your paper. As you complete a step, click on the
to see the
correct response. If yours is correct, move on to the next step. If yours
is not correct, read the explanation. Condense the following expression.
log3 5 + log3 9 + 4 log3 3
The 4 in front of the log is the exponent for 3.
log3 5 + log3 32 + log3 34
log3 5 + 2 + 4
Write it as an exponent. Example: 3 ln 5 is ln 53
You must recognize that 9 is a power of 3,
the base of the log.
.
Once exponents are taken care of, apply
properties
from left to right. Notice that 9 is 32 . The base is
3, So the log of 32 to the base of 3 is 2!! the
same is true of the next term. It simplifies to 4.
log3 5 + 6
The next property is arithmetic ……..
2 + 4 =6 ….. Note the first term cannot be simplified
any further. 5 is not a power of 3, the base.
Read all directions.
Write the steps on paper then click the
to see the correct response. If
yours is correct, go to the next step If it is not, read the explanation.
Write the expression in expanded form. Show each step.
ln 3x2
ln 3 + ln x2
ln 3 + 2 ln x
The logarithm of a product may be rewritten
as the sum of 2 logs. ln A . B is ln A + ln B.
Do not do the exponent first. The 2 goes only
with the x.
The logarithm of a power may be rewritten
as a product
ln Cd = d . ln C
Read all directions.
Write the steps on paper then click the
to see the correct response. If
yours is correct, go to the next step If it is not, read the explanation.
Write the expression in expanded form. Show each step.
log5 (
(3x4)
/ 7
)
log5 3
x4
- log5 7
log5 3 + log5 x4 - log5 7
log5 3 + 4 log5 x - log5 7
The logarithm of a quotient may be rewritten
as the difference of 2 logs.
ln A /B is ln A - ln B.
The logarithm of a product may
be rewritten as the sum of 2
logs. ln A.B is ln A + ln B.
The logarithm of a power may be rewritten
as a product
ln Cd = d . ln C
What did you learn????
Condense and expand the expressions in the left column as directed.
Click the
in the right column for the answer.
•
condense:
5 log y + 3 log 10
• log 1000y5
•
condense:
ln 64 + 2 ln ¼ - ln 4
•
•
expand:
log4 64y4
•
3 + 4 log4 y
•
expand:
ln 3xy
•
ln 3 + ln x + 3 ln y
3
0
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