Section 5.6Laws of Logarithms

(Day 1)

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Laws of Logarithms:let b be a positive number other than

onelet M and N be positive real numbers

1. log log logb b bMN M N

2. log log logb b b

MM N

N

3. log log iffb bM N M N

4. log log for any real numberkb bM k M k

Beware!!!!

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log log log log

loglog lo

1) log log log

but

2) log log log

gl

but

og

M N M N

MM N

N

MN M N

MM N

N

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Ex. 1: Express in terms of log M and log N:

6

4

. log

. ln

a N

c M N

53

5

2 3

. log

. log

b M N

Md

N

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Ex. 2: Express as a rational number or single logarithm: (work backwards)

. log 3 log 4

1. 2 log 5 log 64

3

a aa

c

66

1. log9

2

log. 3log

2

b

nd m

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Ex. 2: Express as a rational number or single logarithm:

. log 6 log 5 log 2 . log 3 log 6 log 5b b ba b

Helpful log values:

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11 log10 1 log

101

2 log100 2 log100

3 log1,000

(You may need to substitute these into log expressions)

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Ex. 3: Simplify: (ln y=k and ek=y) (log y=k and 10k=y)

3 4logb. 10 x1

ln2a.x

e1

ln2

1ln

2

1ln ln

21

2

1

2

x

x

e y

y x

y x

e x

3 4log

4

4

4

3 4log 4

10

log 3 4log

(substitute 3 log1,000)

log log1,000 log

log log1,000

1,000

10 1,000

x

x

y

y x

so y x

y x

y x

x

Homework:

p200 (w) #2-22 even

24-28 even (a and c only)

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