W16D1 Log Review and Graphing
Warm Up
1.
log2 8
6.
log2 64
2.
log2 16
7.
log5 625
3.
log3 9
8.
log5 25
4.
log3 27
9.
log3 81
5.
Evaluate8 · 16
10.
.Evaluate9 · 27
W16D4 CW Logarithms
Inquiry Worksheet - add a line about what is 8x16 or 9x27,
change 10-12 to 3125
change Rewrite to ”argument” and put it above number 1 and keep above 13 but say 13,
delete 15
17 816 18 814 19 810
only use top half of WS for now
1.
3
4.
2
2.
4
5.
3
3.
4+3
6.
2+3
10.
5
7.
6
8.
4
11.
2
9.
6-4
12.
5-2
13.
14.
19.
20.
4
15.
12
17.
16
16.
24
18.
0
2
21.
5
-2
22.
-5
8
Lesson 42 Logarithm Properties
Top half of the worksheet on overhead to show each property.
Summarize properties from the worksheet
Product Property logb (m · n) = logb m + logb n
Quotient Property logb
Inverse Property logb
m
n
m
n
= logb m − logb n
= − logb
n
m
Power Property logb ma = a logb m
The logs MUST have the same base to condense or expand!!
EX 1:
Expand
log3 9x4
log3 9 + log3 x4
log3 9 + 4 log3 x
2 + 4 log3 x
EX 2:
Expand You Try
9xy 3
4z
log5 9 + log5 x + 3 log5 y − log5 4 − log5 z
log5
EX 3:
Condense
5 log y − log z − log 7 + log x
log
EX 4:
y5
− log 7 + log x
z
xy 5
log
7z
Condense You Try
2 log7 x − log7 27 + log7 3
log7 3x2 − log7 27
3x2
27
x2
log7
9
log7
EX 5:
Simplify given that
log3 5 = 1.46
log3 8 = 1.89
log3 6 = 1.63
log3 30
log3 (5 · 6)
log3 5 + log3 6
1.46 + 1.63 = 3.09
EX 6:
log3 120
log3 (5 · 8 · 3)
log3 5 + log3 8 + log3 3
1.46 + 1.89 + 1 = 4.35
EX 7:
log3
4
3
log3
8
6
log3 8 − log3 6
1.89 − 1.63 = 0.26
Groupwork bottom half of the worksheet
Condense
CONDENSE (skip 28, 30?)
27.
log
28.
SKIP log9
3
x
log
y5
29.
30.
SKIP log6
31.
√
ln z 3 xy
32.
33.
34.
35.
36.
Expand
86
1130
4
11
7
106
324
log4 x3 y 9
5
a
log4
b6
√
log9 z xy
4
11
log2
66
√
3
log7 z xy
EXPAND
9.
1 + 6 log6 5
1
+ log4 11 + 4 log4 7
10.
2
3
11. 5 log6 c + log6 a
2
12. 10 ln 5 − 5 ln 2
18 log5 x − 6 log5 y
3
14. 3 log4 7 + log4 2
2
15. log2 y + log2 v + 2 log2 w
13.
16.
18 log9 12 + log9 7
3
17. 5 log9 c + log9 a
2
Exit Pass
1. Expand the expression and simplify log2 32x4
2. Rewrite in condensed form and simplify 2 log4 y − 3 log4 3 + log4 5x
3. Condense the expression and simplify log4 64 − log4 2
1. log2 32 + 4 log2 x = 5 + 4 log2 x
5xy 2
27
1
3. 3 - = 2.5
2
2. log4
Growth and Decay Word Probs 1. Bacteria in a culture are growing exponentially with time, as shown in the table below.
Days
Bacteria
0
2000
1
1500
2
1125
3
843.75
Write a function for the bacteria’s growth or decay.
What would the y-intercept be?
What would the asymptote be?
2. Tell whether the function represents exponential growth or exponential decay. Find the y-intercept and also the horizontal
asymptote for the function:
Movie tickets now average $9.75 a ticket, but are increasing 15% per year. How much will they cost 5 years from now?
A powerful computer is purchased for $2000,but on the average loses 20% of its value each year. How much will it be worth 4
years from now?
Dinner at your grandfather’s favorite restaurant now costs $25.25 and has been increasing steadily at 4% per year. How much
did it cost 35 years ago when he was courting your grandmother?
If a gallon of milk costs $3 now and the price is increasing 10% per year, how long before milk costs $10 a gallon?
The number of bacteria present in a colony is 180 at 12 noon and the bacteria grows at a rate of 22% per hour. How many will
be present at 8 p.m.?
6. A house purchased for $226,000 has lost 4% of its value each year for the past five years. What is it worth now?
7. A 1970 comic book has appreciated 10% per year and originally sold for $0.35. What will it be worth in 2010?8. A Honda
Accord depreciates at 15% per year. Six year ago it was purchased for$21,000. What is it worth now?
9. Inflation is at a rate of 7% per year. Today Janelle’s favorite bread costs $3.79. What would it have cost ten years ago?
10. Ryan’s motorcycle is now worth $2500. It has decreased in value 12% each year since it was purchased. If he bought it four
years ago, what did it cost new?
11. The cost of a High Definition television now averages $1200, but the cost is decreasing about 15% per year. In how many
years will the cost be under $500?
Next Day
2. Solve 2log 6 = 13 log 27 = log x
x = 12
log3 27 + log3 2 − log3 2 = 3
Start CW Simplify Logs Worksheet File Name W2D2 Log Practice half sheet
Answers to W2D2 Log Practice Half Sheet
White Board Problems
18.
log7 (7x + 3) = log7 (5x + 9)
19.
log3 (x2 + x − 6) = log3 14
x=3
x=4
20.
log2 (3x + 11) = 5
21.
log(4x − 8) = 3
x=7
x = 252
22.
log3 (6x + 3) + log2 8 = log2 128
23.
log4 64 − log4 (x − 12) = log2 8
x = 13
x = 13
25.
4 log3 (−9x) = 4
x = −4
x = − 13
27.
− 2 log5 (x + 1) = −8
x=0
x = 624
2
24.
log5 (x + 3x) = log5 (−8 − 3x)
26.
log3
28.
1
81
+ log9 (x + 1) = −6 + log6 36
log4 3x + 2 log3 9 = log4 256
29.
2
log4 (x − 6x) = log4 (10 + 3x)
Exit Pass
1. Expand the expression and simplify log2 4(32) = log2 4 + log2 32 = 2 + 5 = 7
2. Condense the expression and simplify log3 54 − log3 2
log3 27 + log3 2 − log3 2 = 3
1. Find the inverse f(x) = 3x
f −1 (x) = log3 x
2. Solve 8 log1 64 + log3 x = log3 27
x = 31
Solve for x log6 4x = 2
x=
1
3
x = −1, 10
Review Log Rewriting
Simplify each of the following logarithms
1. log3 x = 4
1
27
5.Write in Logarithmic Form 2x+14 = 16
2. log16 4
4. log6 4x = 2
7.
log2 32
10.
log4 4
13.
log 41 16
16.
log36 6
8.
3. log3
log3 27
9.
1
11. log4
256
14. log9 3
17.
log5 625
12.
15.
log 1 7
49
6. log4 64 − log2 16
18.
1
64
log 31 27
log8
log8 16
Answers
EX 2:
1. x = 81
2. x =
3. x = −
4. x = 9
5.
1
2
log2 16 = x + 14
6.
7.
8.
3
9.
5
10.
1
11.
13.
−2
14.
16.
1
2
17.
−4
1
2
1
−
2
Condense to solve
3 log5 x − log5 4 = log5 16
3 log5 x = log5 64
x3 = 64
x=4
EX 3:
Condense to solve
log4 x + log4 (x − 6) = 2
log4 (x2 − 6x) = 2
x2 − 6x − 16 = 0
x=8
1
3
x = −1
4
12.
−2
15.
−3
18.
4
3