9789198233117

COMPLETE SOLUTIONS PACKAGE FOR

MATH MAZE 1

as solved by the author

FARID NOLEN,

B.sc Engineering Physics. Solu ons reviewed and veriямБed by Lova Falk.

105 = 10 · 10 · 10 · 10 · 10 = 100000

(5)

14 = 1 · 1 · 1 · 1 = 1

(6)

91 = 9

(7)

30 =?

(8)

34 = 34 34

2

3

4

= 30 =

3·3·3·3 81 = =1 3·3·3·3 81

=?

24 = 24 27

(9)

7

=2

53 =?

3

=

2·2·2·2 1 = = 0,125 2·2·2·2·2·2·2 8 (10)

53 = 5 · 5 · 5 = 25 · 5 = 125

42

(11)

42 = 4 · 4 = 16

3

43 · 43

(16)

43 · 43 = 4 · 4 · 4 · 4 · 4 · 4 = 43+3 = 46 = 4096

26 · 22

(17)

26 · 22 = 2 · 2 · 2 · 2 · 2 · 2 · 2 · 2 = 26+2 = 28 = 256

910 · 914

(18)

910 · 914 = 9 · 9 · 9 · 9 · 9 · 9 · 9 · 9 · 9 · 9 · 9 · 9 · 9 · 9 · 9 · 9 · 9 · 9 · 9 · 9 · 9 · 9 · 9 · 9 = 910+14 = 924 = 79766443076872509863361

750000 · 78000

(19)

750000 · 78000 = = 750000+8000 = 758000 5

3m · 3h

(20)

3m · 3h = 3m+h R4 · R35

(21)

R4 · R35 = R4+35 = R39 k 3g+1 · k v+10

(22)

k 3g+1 · k v+10 = k 3g+1+v+10 = k 3g+v+11 240 · 230 · 25 = 2x

(23)

240 · 230 · 25 = 2x 240+30+5 = 2x 275 = 2x 75 = x

8y = 8500 · 8 · 82 · 81003

(24)

8y = 8500 · 8 · 82 · 81003 = 8500 · 81 · 82 · 81003 = 85050+1+2+1003 8y = 81506 y = 1506 6

28 = 28 23

3

= 25

(30)

11r · 5b = 112 · 53 · 114 · 55 · 116

(31)

11r · 5b = 112 · 53 · 114 · 55 · 116 = 112+4+6 · 53+5 · 114 · 55 · 116 = 1112 · 514 11r · 5b = 1112 · 58 r = 12 b = 8

230 · 3100 · 540 · 350 · 215 · 510 · 52 = 3x · 2y · 5z

(32)

230+15 · 3100+50 · 540+10+2 = 3x · 2y · 5z 245 · 3150 · 552 = 3x · 2y · 5z 45 = y 150 = x 52 = z

51300 =5 557 24 = 24 29 70 = 1

9

1300 57

=2

5

= 51243

(33)

(34)

(35) 8

73 = 73 73

4

3

=

3

= 70 =

7·7·7 343 = =1 7·7·7 343

1 43

(36)

43 = 43 46

6

=4

3

=

4·4·4 1 1 = = 3 =4 4·4·4·4·4·4 4·4·4·4 4

22 = 30 = 1 32 32 = 32 32 240 = 240 235

3x =

2

35

(37)

= 30 =

3·3 9 = =1 3·3 9

= 25 = 32

3100 325

3x =

3

(38)

(39)

3100 325

= 3100

25

3x = 375 x = 75

4m =

43 410

(40)

9

4

43 = 10 4

m

= 4

7

4m = 4

7

m =

7

33 · 34 = 33+4 32

2

= 35 = 243

210 · 25 23 · 26

2x =

2x =

(41)

(42)

210 · 25 23 · 26

= 210+5

3 6

2x = 2 6 x = 6

3x · 4y =

310 · 320 · 415 412 · 41 · 33

3x · 4y =

(43)

310 · 320 · 415 412 · 41 · 33

= 310+20

3

· 415

12 1

3x · 4y = 327 · 42 x = 27 y = 2

7R =

71000 · 72500 7500 · 7400

(44) 10

7R =

71000 · 72500 7500 · 74000

= 71000+2500 = 7 x =

500 4000

1000

1000

06 04

(45)

0 is undefined or indeterminate. for more info please search google: “division by zero” 0

3x · 7y · 8k =

32 · 460 · 810 · 850 310 · 73 · 825

3x · 7y · 8k = =

(46)

32 · 460 · 810 · 850 310 · 73 · 825 32

3x · 7y · 8k = 3

10

8

x =

8

y =

3

· 1 · 810+50 73

·7

3

25

· 835 ·

k = 35

G0

G0 =

(47)

G1 = G1 1 G

1

= G0 = 1 if G 6= 0

11

0 is undefined (indeterminate. for more info please search google: “zero divided by zero” 0

00 =?

(48)

00 is undefined. For more info please search google: “zero to the zero power”

9x =

918 913

9x =

(49)

918 913

= 918

13

9x = 9 5 x = 5

4x =

42 49

4x =

(50)

42 49

4x = 4 2 4x = 4 x =

54 5 = x 5 0

9 7

7

(51)

12

50 =

54 5x

50 = 5 4

x

0 = 4

x

x = 4

7x =

1 712

7x =

(52)

1 712

7x = 7 x =

12

12

x = 30

(53)

30 = 1 x=1 2 x = 82 · 2 3 · 4 3

(54)

2x = (8)2 · 23 · (4)3 2x = (23 )2 · 23 · (22 )3 2x = 23·2 · 23 · 22·3 2x = 2 6 · 23 · 26 2x = 26+3+6 2x = 215 x = 15 13

5x = (25)4 · (125)2 5x = (52 )4 · (53 )2 5x = 52·4 · 53·2 5x = 5 8 · 56 5x = 58+6 5x = 514 x = 14

2x · 3y = 163 · 812 · 93 · 8

(59)

2x · 3y = (16)3 · (81)2 · (9)3 · (8) = (24 )3 · (34 )2 · (32 )3 · 23 = 212 · 38 · 36 · 23 2x · 3y = 212+3 · 38+6 x = 15 y = 14

3m · 4n = 12

(60)

12 = 3 · 4 = 31 · 41 3m · 4m = 3 1 · 41 m = n=1

2x = 40963 · 644 · 1284

(61)

15

5x

= (64)2 · 49 · (4)3

16 3

= (43 )2 · 49 · 43 = 43·2 · 49+3 = 46+12 5x

(42 ) 3

= 418

5x

42· 3

= 18

10x = 18 3 x=

18 · 3 10

x=

54 = 5, 4 10

2x =

210 · 43 84 · 25

2x =

(64)

210 · (4)3 (8)4 · 25

=

210 · (22 )3 (23 )4 · 25

=

210 · 26 212 · 25

= 210+6 2x = 2 x =

2x · 3y =

12 5

1

1

340 · 210 · 23 6 · 70

(65)

17

2x · 3y =

340 · 210 · 23 (6) · 70

=

340 · 210 · 23 (2 · 3) · 1

= 210+3

1

· 340

1

2x · 3y = 212 · 339 x = 12 y = 39

82 · 302 · 92 · 70 · 52 · 72 2 ·3 ·5 ·7 = 49 · 125 · 27 · 64 x

y

z

u

2x · 3y · 5z · 7u =

(66)

82 · 302 · 92 · 70 · 52 · 72 49 · 125 · 27 · 64

=

(23 )2 · (2 · 3 · 5)2 · (32 )2 · (2 · 5 · 7) · 52 · 72 72 · 53 · 33 · 26

=

26 · 22 · 32 · 52 · 34 · 2 · 5 · 7 · 52 · 72 26 · 33 · 53 · 72

=

29 · 36 · 55 · 73 26 · 33 · 53 · 72

= 29

6

· 36

3

· 55

3

· 73

2

2x · 3y · 5z · 7u = 2 3 · 33 · 52 · 71 x = 3 y = 3 z = 2 u = 1

(56 )4

(67) 18

3x · 8y · 11z = ((360 · 8100 · 11500 )3 )2 = (360 · 8100 · 11500 )3·2 = 360

cdot6

· 8100·6 · 11500·6

3x · 8y · 11z = 3360 · 8600 · 113000 x = 360 y = 600 z = 3000

2x · 3y = (23 · 34 )2 · (35 · 32 · (22 )3 )10

(76)

2x · 3y = (23 · 34 )2 · (35 · 32 · (22 )3 )10 = 26 · 38 · (37 · (22·3 )10 = 26 · 38 · 37 · 22·3·10 = 26 · 38 · 370 · 260 3x · 3y = 266 · 378 x = 66 y = 78

2x · 3y =

162 · 92 (34 )10 · 276

(77)

21

4

3x · 5

5 2y

=

92·3·4 · 252·3 · 453 15 · 75

=

(3 · 3)24 · (5 · 5)6 · (3 · 3 · 5)3 (3 · 5) · (3 · 5 · 5)

=

(32 )24 · (52 )6 · (32 · 51 )3 32 · 53

=

348 · 512 · 36 · 53 32 · 53

= 348+6 4

3x · 5

5 2y

2

· 512+3

3

= 352 · 512

4 = 52 x

4 = 52x x =

4 52

5 = 12 2y 5 = 12 · 2y 5 = 24y y =

(220 )x = 25

5 24

(80)

(220 )x = 25 220·x = 25 20x = 5 x =

5 20

x =

1 4 24

25w · 36x · 57y · 78z = 7 · 4500 = 7 · 3 · 1500 = 7 · 32 · 500 = 7 · 32 · 5 · 100 = 7 · 32 · 5 · 25 · 4 = 7 · 32 · 5 · 52 · 22 25w · 36x · 57y · 78z = 22 · 32 · 53 · 71 5w = 2 2 5

w =

6x = 2 x =

2 6

x =

1 3

7y = 3 3 7

y =

8z = 1 1 8

z =

25x · 36y

v u u 4 =t

24 · 42 2

4

23 · 25

5

!6

(94)

30

COMPLETE SOLUTIONS PACKAGE FOR

MATH MAZE 1 Farid Nolen was studying Engineering Physics at Chalmers University of Technology in Sweden in 2005 when he founded the non-profit math mentor organization Intize. In less than a year the initiative led to a government decision in Norway.

The unique mathematics mentorship model is now being implemented by the Norwegian Ministry of Education and Confederation of Norwegian Enterprise nation-wide on all colleges and universities as "ENT3R", which also won the international 2010 Global Best Award in the category Developing the Future Workforce. Since 2007 Farid has worked as an educational consultant, delivering thousands of inspirational talks and work shops to more than 80,000 people of all ages and backgrounds in 22 countries. Farid was awarded a scholarship by the King of Sweden in 2013 for "Young Leadership with strong values". As a result of Mathivation World Tour 2009, Farid established a Mathivation Center at the Asian Institute of Technology (AIT) in Thailand. Farid has since published an inspirational book on the use of Mathematics in our lives. called "Says Who? From imitator to innovator - and what's math got to do with it?". Farid is also the author of Math Maze; the first math book of its kind, accessible to students worldwide as it includes no words at all and can be understood regardless of language skills.

as solved by the author

NOLEN EDUCATION 2017 Hammaro Sweden www.mathmaze.org

FARID NOLEN,

B.sc Engineering Physics. Solu ons reviewed and corrected by Lova Falk.