Warm-Up

1
Warm-Up
1) Write in exponential form.
2) Write in logarithmic form.
log279 x
5x 2003
3) Evaluate.
4) Write the Equation that models this
situation The current world population of
Oompa-loompas is 7,986. If the Ooompa-loompa
population grows steadily at a rate of 19 per
year, what will their total population be in 10
years?
2
Agenda

• Warm-Up/Check HW
• Go over HW
• Notes Properties
• of Logarithmic functions
• HW
• Quiz on Monday!

Mon May 7th Test 8
3
8.5 Properties of Logarithms
4
Properties of Logarithms
loga1 0
because a0 1
logaa 1
because a1 a
logaax x
If loga x loga y
then x y
Product Property
Quotient Property
Power Property
Change-of-Base
5
Remember Common Logarithm??
log10
Is the common logarithm
This is the LOG button on the calculator
Sometimes were lazy and we dont even write the
base
log107 log 7
6
Basic Properties of Logarithms
1) loga1 0
because a0 1
2) logaa 1
because a1 a
7
3) One-to-one Property If loga x loga y
then x y
8
Product Property
Express as a sum of logarithms.
loga M loga N
1) loga MN
logb A logb T
2) logb AT
log M log A log T log H
3) log MATH
9
Ex.
Express as a single logarithm
4) log5 19 log5 3
log5 (193)
5) log C log A log B log I log N
log CABIN
10
Ex.
Express as a sum of logarithms, then simplify
6) log2 (416)
log2 4 log216
2 4
6
11
Ex. 7
Use log53 0.683 and log57 1.209 to
approximate
log5 (21)
log5 (37)
log5 3 log5 7
0.683 1.209
1.892
12
Quotient Property
13
Ex.
Express as the difference of logs
2)
14
Ex. 3
Use log53 0.683 and log57 1.209 to
approximate
log5 3 - log5 7
0.683 - 1.209
-0.526
15
Power Property
16
try these
conclusions...
17
Ex.
Express as a product.
-5 logb9
4)
5)
18
Ex. 6
Use log53 0.683 and log57 1.209 to
approximate
log5 72
log5 49
2 log5 7
2(1.209)
2.418
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Ex. 7
log105x3y
Expand.
log105
log10y
log10x3
log105
log10y
3 log10x
20
Ex. 8
Expand

• Simplify the division.

• Simplify the multiplication of 4?

• Change the radical sign to an exponent

• Express the exponent as a product

21
Ex.
Condense.
9)
10)
22
Ex 11
Condense

• Express all products as exponents

• Change the fractional exponent to a radical sign.

• Simplify the subtraction.

• Simplify the addition.

23
Warning!!! Be careful!!!
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• Worksheet
• Quiz Monday over exponential equations (are they
  decaying or growing?), word problems, compound
  interest, simplifying logarithms, properties of
  logarithms (simple ones).

25
Change-of-Base
this allows us to change from any base to base 10
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Ex. 1
Evaluate. Round to four decimal places.
1.7712
Be careful about the parenthesis in the
calculator
log(7) / log(3)
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Ex. 2
Evaluate. Round to four decimal places.
0.2626
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Assignmentpage 49614-20 even, 30-70x4