A Tutorial on Logarithms Chapter 8 Section 8'5

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A Tutorial on LogarithmsChapter 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.

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Logarithm RulesThese 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.

• 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!!!!
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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
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)
ln (5/9) ln 32
The next property is . ln C ln D is
equivalent to ln C . D also 3 squared is 9.
ln (5/9) . (9)
The final step is simple arithmetic. 5 /9 . 9
is 5
ln 5

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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.
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.
log3 5 log3 32 log3 34
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 2 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.

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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

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.
ln 3 ln x2
ln 3 2 ln x
The logarithm of a power may be rewritten as a
product ln Cd d . ln C
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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 )

The logarithm of a quotient may be rewritten as
the difference of 2 logs. ln A /B is ln A -
ln B.
log5 3 x4 - log5 7
log5 3 log5 x4 - log5 7
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
log5 3 4 log5 x - log5 7
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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
• condense ln 64 2 ln ¼ - ln 4
• expand log4 64y4
• expand ln 3xy3

• log 1000y5
• 0
• 3 4 log4 y
• ln 3 ln x 3 ln y

click me!
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survey on how to improve this tutorial.
End