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11-30-15
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AM6.1c To apply Laws of Logarithms
Daddy, look at the kitties!!!
1
OPENER:
Convert to exp onents :
log 7 H  59
ln 2  F
H7
59
2e
F
Convert to log s :
5p  Q
p  log5 Q
e2  V
2  ln V
2
ANSWERS to last night’s assignment:
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Active Learning Assignment?
4
LESSON:
Law of Logarithms. If M &N are
positive real numbers and b >0, ≠ 1
Exponent Rule:
*
1. log b M  log b N  log b MN
bxy  bx  b y
Ex. log5 2  log5 x  log5 2x
The sum of the logs is the log of a product.
M
*
2. log b M  log b N  log b
N
y
Ex. log3 y  log3 9  log 3
9
b
xy
x
b
 y (b  0)
b
The difference of the logs is the log of a quotient.
5
*
3. log b M  log b N  M  N
b
Ex.
b
log 2 x  log 2 9  x  9
2
2
*
4. k  log b M  log b M k
Ex.
bx  by  x  y
b
xy
 b

x y
3

log
x
3 log 7 x
7
log 7 x  log 7 x  log 7 x
log 7 x  x  x
Now, remember log b b
log 7 x 3
x
 x?
That’s because log b b x  x  log b b  x 1  x
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Write each expression in terms of log M and log N
(EXPANDED FORM, no radicals).
1. log M 2 N
log M  log N
M
2. log
N
2
2 log M  log N
M2
3. log 6
N
3
2
3
M
log 6
N
1
2
log M  log N
1
2
1
1
log M  log N
2
2
2
3
log M  log N6
2
log M  6 log N
3
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Write each expression as a SINGLE LOG
(no rational exponents).
2. log12  5log P
1. log 2  log C
log12  log P
5
log 2C
1
4
3. 5log T  log Q  log H
2
3
1
2
log T  log Q  log H
5
4
3
log T 5  log Q  log 3 H 4
12
log 5
p
log
T5 Q
3
H4
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Active Learning Assignment:
P.200 1-6, all; 7-17 odds
WOW:
Being mature means doing stuff that
needs to be done or that you are asked to
do, even if you don’t want to.