MHF4UI Exponential and Logarithmic Functions Review

Part A: Short Answer

1 . The special name given to the logarithm (a) with base 10 is

_________________________

(b) with base e is

__________________________

2. Write the following in logarithmic form. x3’ =7

3 . True or False? If false change the left side or right side of the identity to make it true.

a) log(A — B) = log A — log B b) logy M =

c) 3log(2y) = log(6y) d)log8

log4log 2

4. Write the following as a single logarithm in the form loge X.

a) 4log m — 3log y — log z b) 2log t +3

5. Use the properties of logarithms fully to write the following as a sum/difference of logs.

log (Write your answer without exponents)

6. Evaluate each of the following. Your solutions must show enough steps to illustrate a fullunderstanding of the definitions and properties of logarithms. No decimal answers!

a) log4 1024 b) log3 J c) log125 5 d) log15 900 — log15 4

e) 821og83 0 log6 144 + log6 9 g) ln e4

7. Solve the following for x. No decimal answers.

1a)log16x=—. b) logx=6

Part B: Show all your work.

1 . Evaluate the following showing all your work. Do not use the change of base identity. No decimalanswers.

log5 (125 x J)— log2 (0.25)

log7 (49)2. Solve the following for x.

a)log7(x—4)+log7(x+2)=1 b) 2log3x=log3128—3log32

c) log2(x — 4) = 3 + log2(x + 2) d) log4(log3 x) = 2

e) log5 x + log8 x = 3 (Ans to 2 dp) f) ln(x + 5) — ln4 = 2 (Answer to 2 dp)

3. Solve the following giving your answer to 2 decimal places if necessary.

a) 53X 4=17 b) 4(3)2X+1 =63x

4. A bacteria culture, with 1500 bacteria doubles every three hours.

a) Write an equation that represents the number of bacteria, N, after h hours.b) Using you equation in a) determine the number of bacteria i) after 2 hours. ii) 30 minutes ago.

5. On a long canoe trip water must be drank from the lake. It is not safe to drink directly from the lakeso it must be passed through a ceramic filter. The filter must be cleaned at times so that it remainseffective. The filter loses about 10% of its effectiveness every 6 times that it is used.

a) Write the equation that represents the filters percent effectiveness, E,after it has been used n times.b) How effective is the filter after it has been used 26 times? Give your answer to the nearest percent.c) For safe drinking water it is recommended that the filter be cleaned when its effectiveness has been

reduced to 50%. If this is true, after how many uses should the filter be cleaned?

6. A research assistant made 240 mg of radioactive Lutetium and found there was only 107 mg left after6 months. Assuming that each month has 30 days determine the half—life of Lutetium.Give your answer to the nearest day.

7. The present population of Canada is 34 million., and is growing a rate of about 1.3% per year.a) Write an equation for the population P after y years using base ‘e’.b) Using your equation in a) determine i) the population in 50 years.

ii) when the population will reach 100 million.

8. Factor completely a) — 1O(x + 5’ (x +9)_4 4(x + 5Y’° (x +

b) (x+6)2(x+1o)3+(x+6)2(x+1o)3

9. Yellow Book Math 12

Page 289 # 1 — 6, 8, 9, lOa Page 507 # 1 — 12, 14—26Page 290 # 1 , 2, 4 — 10 (do the evens, then odds — this is a lotPage 286 #3ac of questions for additional practice)

Review Sheet Answers Part A

1. (a) common (b) natural 2. logs 7 = 3. a) F b) T c) F d) F 4. a) loa[ b) log(t2a3)

5 . 4log a — 2log x — log y 6. a) 5 b) -4 c) d) 2 e) 4 g) 4 7. a) b) 8

Review Sheet Answers Part B

1. 2.a) 5 b) 4 c) No Solution d) 316e) 15.21 f) 24.56 3.a) 0.53 b) 0.78 4.b)i) 2381 ii) 1336

5.b) 63% c) 39 uses 6. 154 days 7. b) i) 65.1 million ii) 83 years

8. a) —2(x+5)”(x+9)5(7x+55) b)i(x+6)2(x+1O)3(5x+42)

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