BAB 1 Bentuk Pangkat, Akar, Dan Logaritma

Kunci Penyelesaian Matematika SMA Jl.1A – Sukino Bab 1 | page 1

L K S 1

A. Evaluasi Pengertian atau Ingatan

1. D43 3 3 3 3 3 81

2. C5( 1) ( 1) ( 1) ( 1) ( 1) ( 1) 1

3. D10

10kali

( 1) ( 1) ( 1) 1

4. A7

7kali

( 2) ( 2) ( 2) 128

5. A( 7) ( 7) ( 7) 343

6. E

31 1 1 1 14 4 4 4 64

7. B5243 3 3 3 3 3 3

8. C3343.000 70 70 70 70

9. D2 2 2 22 2 2 ( ) a b c ab ac bc a b c

10. A2 2 22 ( ) x xy y x y

B. Evaluasi Pemahaman dan PenguasaanMateri

1. a) 2 3 55 5 5 5 5 5 5 5 b) 2 4 73 3 3 3 3 3 3 3 3 3 3 c) 2 5 82 2 2 2 2 2 2 2 2 2 2 2

d) 2 41 1 1 1 15 5 5 5 5

1 1 15 5 5

615

e) 2 41 1 17 7 7

1 1 1 1 17 7 7 7 7

4

kali

717

f)5

23

7 7 7 7 7 7 77 7 77

g)7

34

5 5 5 5 5 5 5 55

5 5 5 55

h) 2 5 7(0,5) (0,5) (0,5)

5

(0,5) (0,5) (0,5) (0,5) kali

14

7

(0,5) (0,5) (0,5)kali

2. a) 30 0 0 0 0 b) 50 0 0 0 0 0 0 c) 40 0 0 0 0 0 d) 6

6

( 1) ( 1) ( 1) 1 kali

e) 9

9

( 1) ( 1) ( 1) 1 kali

f) 5

5

( 1) ( 1) ( 1) 1 kali

3. a) 2 3 4 5 5 5 5 55 5 5 55 5 5 5

b) 7 4 5 67 4

5

3 3 3 33 3 3 3

3 3

kali kali

kali

c) 5 2 3 13 3 3 3 3 33 3 3 3 33 3 3 3 3

d) 7 2 3 25 5 5 5 5 5 55 5 5 55 5 5 5 5

e) 2 3 5 2 2

5

(3 ) 3 3 3 3 3 kali

11

6 5

3 3 3 3 3 kali kali

f) 2 3 2 2 2(7 ) 7 7 7 67 7 7 7 7 7 7

g) 2 3 3 2 3 2 3 2 3(3 ) (3 ) (3 ) (3 ) m n m n m n m n

6 9

27 kali kali

m m n n

6 927 m n

h)3 5 3 5

3 5 2 ( ) ( )( ) x y x yx y xyxy

6 10

kali kali

x x y y

xy5 9

5 9

kali kali

x x y y x y

BAB 1BENTUK PANGKAT, AKAR,

DAN LOGARITMA


L K S 2

i) 2 4 2 3 3(2 2 ) (2 2 )

2 4 2 4

3 3

(2 2 ) (2 2 )

(2 2 ) (2 2 )

412

8

2 2

22 2

kali

kali

j) 3 3 3(4 ) 4 4 4 4 y y y y y

4. a) 7

7

( 3) ( 3) ( 3) kali

b) 51 1 13 3 3

5

( ) ( ) ( )

kali

c) 3(1,75) 1,75 1,75 1,75

d) 5

5

(10,5) 10,5 10,5 kali

e) 7

7

( 0,8) 0,8 0,8 kali

f) 4 45 41 41 41 41 4112 12 12 12 12 12(3 ) ( )

g) 5 58 8 8 8 8 823 3 3 3 3 3 3(2 ) ( )

h) 6 68 8 817 7 7 7

6

( 1 ) ( ) ( ) ( )

kali

5. a) 3 3( 2 ) ( 2 ) ( 2 ) ( 2 ) 8 a a a a a

b) 6 6

6

( 3 ) ( 3 ) ( 3 ) 729 kali

b b b b

c) 2 3 4 2 3 2 3

4

(6 ) (6 ) (6 ) kali

x y x y x y

8 121.296 x y

d) 3 4 3 3 4 3 4 3 4 9 12(3 ) (3 ) (3 ) (3 ) 3 a a a a a

e) 2 2 2 2 6

382 2 2 2

y y y y y

f) 2 2 2 2 2 8

2 2 2 2 2 8

43 3 3 3 3 81 x x x x x xy y y y y y

C. Evaluasi Kemampuan Analisis

1. a) 2 2 2( ) 2 x y x xy y

b) 2 2 2( ) 2 x y x xy y

c) 3 3 2 2 3( ) 3 3 x y x x y xy y

d) 3 3 2 2 3( ) 3 3 x y x x y xy y

e) 2 2( ) ( ) x y x y

2 2 2 22 2 4 x xy y x xy y xy

f) 2 2( ) ( ) x y x y2 2 2 22 2 x xy y x xy y

2 22 2 x y

2. a) 2 2 2 2( ) 2 a b c a b c ab2 2ac bc

b) 2 2 2 2( 3 ) 9 2 x y z x y z xy6 6xz yz

c) 2 2 4 3 2( 3) 2 5 6 9 x x x x x x

d) 2 2 2( ) ( ) ( ) a b c a b c a b c2( ) 8 a b c ac

e) 3 3 2 2 3( 2 ) 6 12 8 x a x ax a x a

f) 3 3 3 2 2( ) 3 ax by a x a bx y2 2 3 33 ab xy b y

3. a) 2 22 2 221 1 1( ) 2 x

x x x xx x x

b) 2 22 2 221 1 1( ) 2 x

x x x xx x x

c)2

2 33 3 3 31 1( ) x x

x x x xx x

33 3 13 x x

x x

d)2

2 33 3 3 31 1( ) x x

x x x xx x

33 3 13 x

x xx x

4. a) 8 420.736 2 3 b) 6 611.390.625 5 3 c) 5161.051 11d) 3 32.744 2 7

5. a) 5 3223 243

b) 3 33 125 1 11000 8 512(0,125)

c) 4 44 3 8112100 25 390.625( 0,12)

d) 4

4

4 (513)4 513100 (100)

(5,13)

A. Evaluasi Pengertian dan Pemahaman

1. D5

5

1 132433

2. D7

7

1 10

00 tak terdefinisi


3. B5

5

1 1( 1) 11( 1)

4. D8( 1) 1

5. D2 6

2 3 2 6

1 1 1(0,001) 10(0,001) (10 ) 10

6. C7

7

110 0,0000001

10

7. D3

3

1 1 5125 5

8. C

34

1 43

9. B

2 42 93

1 1 94

10. E3

3

15 125

5

11. B

3 11 644

1 1 64

12. C70,000000256 2,56 10

13. C8123.000.000 1,23 10

14. C2

2 2 2 2

1 1 1(5 )

25 5 (5 ) a

a a a15. E

33 1 31

7317

1 7 7


1. a) 55

1 aa

b) 3 23 2 5

1 1 1 a aa a a

c)3

4 3 34 3 4 4

1 1 1 1 b

b b bbb b b b

d)5

2 3 52 3 5 2 3

1 3 13

3

xa x x

a x x a x5 2

2 3 23 3

x xa x a

e)2 7

2 7 1 8

p pp p p p

p

f)5

5 10 310 3 8

1

pp p p

p p p

2. a) 0 1 5 71 1 12 1;2 ;2 ;22 32 128

b) 0 2 41 16 1;6 ;6 ;36 1.296

6 1646.656

c) 2 0 2 31 1 1 13 3 3 3

1 ; 1; 9; 279

d) 1 0 22 2 25 5 5

5 4; 1; ;2 25

325

1258

3. a) 2 2 2 0256 16 ;64 8 ;4 2 ;1 2

b) 2 4 6 81 1 1 12 ; 2 ; 2 ; 2

4 16 64 256

c) 5 3 216.807 7 ;343 7 ;49 7 ; 1 07 7 ;1 7

d) 1 2 31 1 111 ; 11 ; 11 ;

11 121 1.331

4111

14.641

4. a) 22 2 2

1 1 ( )2 ( )

a ba ab b a b

b) 1 2 32 3

1 1 1 a b ca b c

80

c) 2 2 2

12 2 2 x y z xy xz yz

2

1( )

x y z

2( ) x y z

d)1 2 3 4

2 3 4

1 2 3 4 2 3 4 a b c da b c d


L K S 3

5. a) 77

33 b

b

b)2

3 23

y

x yx

c)2

2 5 75 7

12 2

a

a b cb c

d) 1 1 44

b

a bc dacd

e)3

3 2 12

14 4

a

a b cb c

f)2 2 1 2 3 3 2

1 3 2 3

3

9 3 3

m n k m mk m k

m nk nn k n


1. A4 5 3 7 4 3 5 7 2(5 )(2 ) 10 10 a b a b a b ab

2. A

33

33

0 1

1 3 1 323 3 13 22 32

(0,6) (0,1) 1 10

( 3)

3 3 3 1

9 9 9 39 3 6 22 3 3

3. A12 2 7

12 5 2 2 75

3 9 3 (3 )3

a aa a a

a

12 4 4 143 3 a a

12 4 4 14 2 13 39

a a

4. B

2 2 22 12 6 1 51 1 42 4 4 4 5

163 1

25

5. D

2 2

1 213333

3 9 13 3 3 3 3 8 123 3 3 13

x

xx x x x

x x xx

6. A

1 36 5 9 2 9 6 3 3

9 2 6 5 5 2 3

3 81 27 3 381 3

a b a b a a aba b a b b b

7. E4 6 6 8 4 4 6 8

7 4 7 6

2 5 (6 3 ) 2 (6 3 )11 5 2 11 5

6 866 3 40.095 729 3

55 55

8.22 2

3 3

9 3 (3 ) 27 1273 2

xx x

y

9. B

a b b c c aa b c

b c a

x x x

x x x2 2 2

2 2 2

a ab b bc c ac

ab b bc c ac a

x x x

x x x2 2 2 2 2 2 a ab ab b b bc bc c c ac ac ax 0 1 x

10. D1 1 1 1

1 1 1 1

n m

m nn m m n a a

a aa a

1 1

m n m n

m na a a a

a a

m n

m n m n

a aa a a a

1

m n

m n

a aa a

11. D1 1 1

1 1 1 1

1 1( )

m n

m nm n1

m nmn

mnm n

12. C4 4 2 2 2 2

2 2 2 2

( )( )

x y x y x yx y x y

2 2 x y

15. D

Diketahui :1

3 xx

22 2

2

22

1 2 13 9

1 9 2 11

xx xx x x

xx

Jadi, 22

111. x

x


18. C2 2

12

32 5 2 3 5 2 5 3 0

(2 1)( 3) 0

atau 3

x x x x xxx x

x x

(i)

221 12 22 21

2

9 94 4

x x

x

1 36 35

(ii) 2 22 2

9 93 4 4(3)(3)

x xx

36 1 35 Jadi, nilai yang memenuhi adalah 35.


1. a) 44

1 66

b)3

3 22

2 2 44

c)2 4

2 4 3 53

3 3 3 33

d)3 4 5

3 4 5 1 2 6 12 6

2 2 2 2 22 2 2

e)2 3 2 2 3 4 3

2 3 2 4 2

(9 3 ) (3 3 ) (3 )(3 27) (3 3 ) (3 )

1212 8 4

8

3 3 33

f)2 4 2 2 6 2

3 2 3 3 5 3

(16 4) (2 2 ) (2 )(4 8) (2 2 ) (2 )

1212 15 3

15

2 2 22

2. a)3 4 4 2 2 6 2

2 5 2 5 3 8

7 3 3 5 3 53 7 5 7 7

d)2 2

5 4 3 5 2 4 3 2 7 3

7 3 1 13 7 7 3 7 3 7

e)2 2 4 3 2 2 4

2 4 2 2 2 4 2 2

8 5 3 (2 ) 5 325 2 9 (5 ) 2 (3 )

6 2 4

4 4 4

2 5 35 2 3

4 6 4 4 4 2

12 3 5

10 2

12 5

f)2 4 3 2 8 6

2 2 5 3 4 15

(2 ) (2 ) 2 2

(2 ) (2 ) 2 2

4 15 8 6 25

1 1

2 2

3. a) 1 1 1 0 1 1 13 (6 6 6 6 ) 3 (6 6 )

16

5 53 (1 ) 3

6 2

b) 1 3 53 5

1 1 13 3 3

3 3 3

4 2

5

3 3 1 912433

c)2 0 6 0

6 2

( 16) (16 16 ) 2 (16 16 )

5 2 5 ( 16)

6 6

2 8 8 64

2 (16 1) 2 15 3 345 2 25 ( 1) 2

d) 2 2 21

1( 3) ( 3) ( 3)

( 3)

9 ( 3) (9 9) 12 18 216

4. a) 9 4 9 4 5b b b b

b) 6 2 6 2 44

1y y y yy

c) 10 6 10 6 44

1m m m mm

d) 12 3 12 3 15x x x x

e)6

3 23 2 2 2 6 2

1 1(2 )(2 ) 2 4

babab a b a

f)

2 4 32 4 3 3 6 12

1 1(3 )

(3 ) 3x y

x y x y

6

1227

x

y

g)2 21 2

2 2 2 22 2 2 4x

y xy x y x y

h)2

3 2 2 2 6 2 63

4 (4 ) 4 16m mn m n m nn

i)24 2 8 8 8

3 6 2 6 66 6

6 36a a a ac c c c

j)3 3 3

4 12 3 3 12 3 125 5 1 1

5 125x x

y y x y x y

5. a) 0(2 ) 1a b

b) 0(14 8 ) 1a b

c) 0 0 1 1 2m n d) 0 07 8 7(1) 8(1) 15x y

e)0 0

2 2 0

3 (3 ) 11

12 (2 )a ab b

f)03 3 0

2 2 0

17 (17 ) 11

154 (54 )

x x

y y


6. a)4 3 3 3 4 3 5 7 8

6 4 5 6 4 10x y z y z y zx y z x x

b)2 3 20 1 3 0 3 0

2 5 5 5

( ) ( )( )a b a b a a b a

a b b b

0 2 2

5 3 2

a ab b

c)3 1 32 3 3 3

3 2 2

( ) ( ) ( 1)ab c a a c a a ca b b

4 3

2

a c

b

d)4 4 3 73 0 0 4 4

3 4 3 32 2 2

x y z x z x z

x z y y

e)3 2 3 3 3 6

0 3 0 3 32 2

m n p p pm p m mn n

f)2 3 3 6 3

4 6 4 2 6

m n n nm n m m

7. a)2 2 23 1 33 4

3 33 4 4

a b c a a

c a a b b c

24 8

3 64 8

a ab c b c

b)2 2 22 3 2 2 1 3 22 4

3 2 2 4 4 2

3 3 39 3x y x y xx y x y y

25 10

2 4

3 9x xy y

c)3 34 3 0 3 5

4 5 44

x y z yz y x z

38 24

4 124 12

y yx z x z

d)4 44 2 2 6

6 3 3 11 4

a b c bab c a c

48 32

2 85 20

b ba c a c

8. a)2

1 2 0 21 11

ab aa b c b

a a

b)2 2

2 22 2 2 2

1 1 x yx y

x y x y

c)2 3

2 3 233

1 1x yx y x

yy

d)

4 3 0 43

1 1m n p mn

4 3 3

3

1m n nn

e) 2 2 3 2 23

1x y z x y

z

2 3 2 3

31x z y z

z

f) 2 1 2 22

1 1m n p pnm

2 2 2

2

m mn npm n

g) 0 2 2 20 2

1( )( )

a b c ca b

22

1(1 )

cb

2 2

21 (1 )

(1 )b cb

h)2

22 2

1 1 ( )( )( ) ( )

a b ca b c ca b a b

i)

1 21 2 22

1 1(2 )(2 )

a

a ba b b

2

2 22

1(2 )ab

a

aab

j) 2

2 32 3 3

1

1 1( )( )

b

a ba b a

2

2

6

3 2 31

1( 1)ab

b

bab


1. a)2

1 2 11 2 3 2

1 1(3 2 )3 2 x y

x yx y

2

2

2

23 2

13 2y x

xy

xyy x

b) 2 2 1( 6) ( 1) 2( 6)( 1)x x x x 2

2( 6) 2( 6)

1( 1)x x

xx

2

2( 6) 2( 6)( 1)

( 1)x x x

x

2

( 6) ( 6) 2( 1)

( 1)

x x x

x

2

( 6)( 8)

( 1)

x x

x


L K S 4

c) 2 1(4 5)( 2) 3(4 5)( 2)x x x x

2

4 5 3(4 5)2( 2)

x xxx

2

4 5 3(4 5)( 2)( 2)

x x xx

2

(4 5) 1 3( 2)

( 2)

x x

x

2

(4 5)(3 7)

( 2)

x x

x

d) 2 2 13( 4) (2 5) ( 4)(2 5)x x x x

2

2

3( 4) 42 5(2 5)

x xxx

2

2

3( 4) ( 4)(2 5)

(2 5)

x x x

x

2

( 4) 3( 4) (2 5)

(2 5)

x x x

x

2

( 4)(5 17)

(2 5)

x x

x

e) 2 2 12( 1) (3 1) ( 1)(3 1)x x x x

2 2

2 2

2( 1) 1 2( 1) ( 1)(3 1)3 1(3 1) (3 1)

x x x x xxx x

2 2

( 1) 2( 1) (3 1) ( 1)( 3)(3 1) (3 1)

x x x x xx x

2.

3 3

3 3 3 3

3 33 3 3 3

1 13 3 3 3

3 3 3 31 1

b aa b a b

b aa b a b

a b b aa b b a

Dengan membagi pembilang danpenyebut di atas dengan 3b diperoleh:

3

3

3

3

33 3 3

3 3 3 3

1 1

1 1

a abb

a ab b

b a bb a b

3. a)

2

2 2

22 2

1 11 2

2 1 1 1

x yx y xy

x yyx x y

x yx y

2 2 2

2 2 2

( )( )

x y x y x x yxy x y y x y

b)2 3 4

2

1 1 12 3 4

2 1 0 1 1 1m m m

mm

m m mm m m

2

4

2

2

1 2

4 4 2 21

1 1m m

mm m

m

mm m m

c) 2 2

1 11 1

1 1

b aa b abb a b aa b ab

a ba b ab

2 2

b ab a

1( )( )

b ab a b a b a

d) 2 2

1 11 1

1 1 2 2

a ba b aba b a bb a ab

a b a bab a b a b

1( )( )

a ba b a b a b

4.2 2 2

1 2 2 2

( ) 4

(4 ) ( )

Lr r L LmrH

m r L

5.2 1 1 2

1 1 1 1 12 1 1 2

1 1( ) d

f f f f

Ff f d f f

1 2

21

21

1 2

1f f d

ff

fff f d


1. A

1 3 1 13 32 28 (2 ) 2 2

2. B44 4 55 5 5 4

5 4

243 32 2 2 1632 243 813 3

3. B

12 63 23 212 6 4 3 7x x x x x x

4. B1 1 1 1 1 1

1 1 1 1ab bc ca b c a

a b c

a b c

b c ax x x x x xx x x x x x

5. A

7 7 32 2 2 7 5 3 1

2 2 2 25 5 12 2 2

3x y x yx y xy

x y x y

6. B

1 1 1 y z xx y y z z x

x y z

1 1 12 2 2

1 1 12 2 2

1x y z

x y z

8. A2 2 23 3 32 4 3 2 1 3 3

1 2 3 2 4 3 6

8 2 2

125 5 5

x y x x

x y y y

2 22 4

2 4

20,16

5

xx y

y


9. E

13

2 36 3 6 6 3 6 233

68 2 2 4x x y x y xyy

10. C

1122

12

21 1 2 2 23 3

2 421 12 2

2 2

4 2 2

(3 )2 2 3 3 22 2(2 )2 2

3 12


1. a)51

3 353 32 (2 ) 2

b)1 12 211

2 (2 ) 2

c)1 23 323 4 (2 ) 2

d)31

5 53158 (2 ) 2

e)31

2 212 2 2 2 f) 01 2

g)124 2 4 1 31

416 2 (2 ) 2 2

h)5 5 74 4 43341

8 32 2 2 2 2

2. a) 21 39

b)133 3 3

c)1 1 12 2 2111

3 3 3 3 3 3

d)355 27 3

e)3414

27 3

f) 01 3

g)82

3 33 2 481 (3 ) 3

h) 2 2 2 2 2 019 9 3 3 3 2 1

i)54 4 4

5 5 5 51 115 51381 243 3 3 3 3 3

j)23 52

3 656

3331 16

27 243

3 39 3

3

9 36 23 3

3. a)1 12 224 (2 ) 2

b)3 34 44 316 (2 ) 2 8

c)2 23 33 227 (3 ) 3 9

d)12

122

1 19

3(3 )

e)3 34 44 381 (3 ) 3 27

f)3 32 22 325 (5 ) 5 125

g)3 35 55 3

3

1 132 (2 ) 2

82

h) 22 3 33 210 10 10 10

i)3

314 64

4

j) 1 12 2

44 1 4 213 3 3 (3 ) 3 9

k)1

22

13 9

3

l)

11 22 2

2

4 2 29 33

4. a)2 3 2 33 34 43 4125 81 (5 ) (3 ) 25 27 2

b)3 2 3 2

3 34 44 316 27 (2 ) (3 ) 8 9 1

c)2 21 13 32 22 39 125 (3 ) (5 ) 3 25 28

d)1 11 13 32 22 3 1 74 27 (2 ) (3 ) 3

2 2

e)3 2 3 2

3 34 44 3 1 1 316 8 (2 ) (2 )8 4 8

f)1 1 1 12 2 2 22 2 749 36 (7 ) (6 )

6

g)3 31 1

2 4 2 4

2 23 3

2 4

3 23

9 16 (3 ) (2 ) 3

28 (2 )

5

3 3322

h)2 21 13 32 2

1 1 43 3 3

12 34

4

525 8 (5 ) (2 )

81 (3 ) 3

3 319 574 43 3 3

i)2 21 13 34 4

1 13 3

16 416

13

364 81 (2 ) (3 ) 916327 (3 )

j)3 1

32

1 1 12 2 2

2 2 3 2 3 1 2

3 22 3 2 6

(3 ) (8 ) 3 2 3 3

23 (4 ) 9 3 (2 )

23 92 2

5.2 413 32 4 1

3 31 11 16 34 2

2 2 42 1 4 116 9 4 2 3 2

2 316 9 4 2 3 2

B

2 32 3 108


6. a)23142 27,22

b)3567 12,46

c)115

3 3 59114 4 5 20

38 1 12,17 10

8 8 8

d)131,76 14 50,69

e)1431

4 434

22 3 0,52

3

f)23 2 1 1

3 2 612

1111 11 1, 49

11

g) 1

3 1684

18

17 7 0,78

7

h) 2

2 453 15

415

118 18 0,46

18

7. a)23

3 3 2 3 17234 4 4 3 12

1 1 1x

x x x xx

b)35 3 31 1 14

5 3 5 3 1513

y y y y yy

c)3 34 4 41

7 5 7 5 35a a a a

d)3 31 1 167 3 7 3 21m m m m

e)3 51 3 1

8 8 4 8458

1y y y yy

f) 13 22 314

3 2 232

2 mm n m nn

g) 343 31 1

2 4 2 412

1 yx y x yx

h)35 3 3 3

5 4 2034

x x xx

i) 1 1 1 73 3 3 3

2

2 2

1 1 1b

b b b b b

j)14

14

44

1a ba b

8. a) 33

1aa

b) 1 1( )a ba b

c) 2 12

1a b

a b

d)12 2a

e)13 35 5

f)12a b a b

g)34

34

4 31a a

a

h)323 1

5215 5

a a aa b

bb

i)1311

3212

3

333

b bb

j)14

14

44 44

1 1a b

a ba b

9. a)123 3

b)544 53 3

c)133 13 1 3 3

3

d)1211 2 2

2

e)2 13 323 x y x y

f)12( )a b a b

g)2

2 1

a bb a

h)2 1 2

2 2

a b cbc a

i)12

133

a ab b

j) 344 3

1 1

bb

10. a)31

2 4 3 91 12 4 8 8

18

x xx x

x

b)2 17 3 2 1 1 19

7 3 2 4212

a aa a

a

c)37 3 1 47

7 3 211 473 21

33 1a a

a aa a

d)31 11 1 1 1

2 8 82 4 2 4

3 3 3 3 518 8 8 8 4 8( )

x y x y x x

xy x y y y

e)2 713 4 4

1 1 1 2 54 4 4 3 12

22x y y y

x y x x

f) 1

3 52 23 3 3

1 1 1 133 3 3 3

22 14

41 1

m n m n n n

m n m n m m

11. a)1 1 12 6 222 2 2 16( )( )a b c a b c a b c 2 53 2a bc


b)

122 2 2 2

2 3 2 53 5

d e f d e fd e fd e f

1 92 2

2 2

53 2

1e

d f df

c) 33 2 3 3x y z x y z

3 131 1 2 21 13 3 3 2 3 62 2x y z xy z

d)3 31

2 2 2

1 1 12 2 2

2

2 3 2 2

( )

( )

a b a b a a

ab ab a b a b b a b b

e)21 132 2

5 32 2

2 2 23

5 3

( )( )x y x y x y x y

x yx y

35 1 2 112 3 2 32 2

13

2 0 1x y x y

y

f)2 2 2 2 2 3 2 9

2 1 3 3 6 3 9 6 2

( )

( )

abc a b c b c

a b c a b c a

5 11

4

b c

a

g)1 1 1 1 1 115 3 2 3 3 62

1 1 1 1 116 3 6 2 52

35

3

x y z x y z y z

x y z x y z x

1 16 2

310

y z

x

h)1 1 11 1 13 3 32 2 2

3 12 2

3 3

3

( )( )a bc ab a b c a b

a b ca bc

31 1 1 1 11 13 2 2 3 2 6 3

1 32 2

3

1

a b a b

c c

12. a)112

12

2 22

1 14 (2 )2(2 )

(terbukti)

b)113

13

3 3

3

1 18 (2 )

2(2 )

(terbukti)

13. a) 12 ( 2) 3x x

1 2 1 12 2 ( 2) 3 3 32 2

x

0 1 11 2 ( 2) 3 1 3

2122

x

21 2 2 3 1 2 x3 22 2 ( 2) 3 8 2 3 3x

b) 2 1 02 2x x x 2 1 02 2( 2) ( 2) 2( 2)

1 12 3

2 2

x

2 1 01 2( 1) ( 1) 2( 1)2 1 2 5

x

2 1 01 2(1) (1) 2(1)2 1 2 3

x

2 1 02 2(2) (2) 2(2)1 1 2 22 2

x

14. a)1 13 32 23 (2 2) (27 4 2)

13 335 35

b) 2 2 2(3 4 12 ) 169 13

c) 3 3 3 3 3 31 2 3 4 5 6 441 21

15. a)12 24 2

2

3(9 ) 3

yx yx y

x

b)

1 4 4 23 3 3 3

23

4 3 2

2 6 2 12

125 5 5 5327 33

x y x y x xyx y yx y

c)

1 3 12 2 2

512 2

0 4 3 2

6 5 2 3

416 2

a b c a b ca bc a b c

512 2

312 2

2 2

53 2

2 4c ca ba b

d)1 12 2

1 12 2

2

2

1( )

( )x y

x y

1 12 2

1

2x y x y

e)11323 2 1 11 1

3 3 34 2 213

( ) x yx z y x z yz

f)1 1 1 1 1 12 2 2 2 2 22 2( )( ) ( ) ( )m n m n m n

1 1 1m n

m n


1. a)31

4 4(2 5)( 1) ( 1)x x x 34

14

1 14 4

2 5 ( 1)( 1)2 5 1 3 4

( 1) ( 1)

x xxx x x

x x


L K S 5

b)1 12 2( 7)(3 5) (3 5)x x x

12

12

12

12

2

7 (3 5)(3 5)

7 (9 25)

(3 5)

x xx

x x

x

c)3 25 5(3 7)( 2) 8( 2)y y y

25

35

3 35 5

3 78( 2)

( 2)3 7 8( 2) 5 9

( 2) ( 2)

yy

yy y y

y y

d)2 13 3(4 1)( 4) 6( 4)m m m

13

23

2 23 3

4 1 6( 4)( 4)4 1 6( 4) 10 23

( 4) ( 4)

m mmm m m

m m

2. a) 53 1 2 13 3 62 2

243 27a b c a bc

52143 62

2

75 13 62

1 23223

64 4 5 73

3

2 2

a b c

a b c a b c

b) 53 1 2 13 3 62 2

243 27a b c a bc

5 53 1 213 3 3 32 2

5132

23

2 11

3 5

3 2

108 108

108 108

a b c a b c

a b a b

c c

c) 53 1 2 13 3 62 2

2243 27a b c a bc

523 3

4 13 3

2 23 1

32 2 4

144

144 144

a b c

a b c a b c

3.71 41 1

3 3 52 4

3 315 5 5

2 3 4 3 5

10 5 4 6

311 1

3 52 4

3 71 45 5 3 5

61 1 1 1 42 2 5 5 3 3

3 715 5 5

2 2

1 1 0

1

2 3 (2 ) (2 ) 2 3

(2 5) 5 3 5

2 3 2 310

55

4.1 11 1225 5 5 (5 ) 5y yx xzz

2 1 2 1

2 12

z zy x y x

x y xyzxy z x y

5. 322 2

2

( )

mLHr L

12

1 12 2

2 2

2 2 2 2 2 2

2 ( )

( )( ) ( )

mL r L

r L r L r L

122 2

2 2 22 ( )

( )mL r L

r L

6. 23 2 343336 36V r

33 6 3 61639

3 6 3 6 2

36 64

2 4

r r

r r

Jadi, 3 236A V .


1. D2 2

2 2

12321 111 111 111 ;2025 45 45 45 ;

3025 55 55 55 ;6561 81 81 81

2. B4375 4375 625 25

77

3. D10 250 2500 50

4. C

176 2.401 176 49 225 15

5. B

248 52 144 248 8 256 16

6. D18225 182,25 1,8225 0,018225135 13,5 1,35 0,135 149,985

7. B2

2

1,21 9 121 10 9 31,1 1,1 121 10


8. A

2 4

2

0,004 0,4 0,4 0,004

4 10 16 10

4 10 0,0016

a b

a b

a abb

9. D1,21 0,01 1,1 0,1 1

10. A12 4 3 4 3 2 1,732 3,464

11. D0,81 4 0,9 2 9

0,0064 6,25 0,08 2,5

12. E0, 204 42 36 60,07 3,4

13. C1 441 214 4 2110 10,5

14. E3

5

0,361 361 10 1,9 10 1900,00169 13169 10 0,13 10

15. E

0,01 0,0064 0,09 0,3

16. E4,5 0,0085 18,9 150,0017 13,5 2,1

17. A27 14

1 1 1169 13 13 13

x x

1 113 13x x

18. C1 1

0,5771,7323

19. E

20. B


1. a) 2 4324 2 3 2 9 18

b) 2 22601 3 17 3 17 51

c) 21681 41 41

d) 21849 43 43

e) 22809 53 53

f) 2 23844 2 31 2 31 62

2. a) 40,3136 3136 10 6 2 22 7 10 0,56

b) 210,89 1089 10 2 2 13 11 10 3,3

c)23,24 324 10 2 4 12 3 10 1,8

d) 40,5184 5184 10

6 4 22 3 10 0,72

e) 41,1025 11025 10 2 2 2 23 5 7 10 1,05

f) 2116,64 11664 10 4 6 12 3 10 10,8

3. a) 13 26 18 45 105 21 2 6 2 2 22 3 5 7 13 24750

b) 169 0,0009 1,21 2025 6 2 6 2 23 5 10 11 13 19,305

4. a) 75, 24 0,71x Kuadratkan kedua ruas diperoleh:75,24 0,5041

74,7359x

x

b) 1872 234 234 1872xx

Kuadratkan kedua ruas diperoleh:2

22

18728 64

234x .

5. a) KPK dari 15, 18, dan 25 adalah 450.Jadi, bilangan kuadrat terkecil yanghabis dibagi ketiga bilangan di atasadalah 900.

b) Bilangan terkecil yang harusdikurangkan dari 549162 agar dapatmenjadi bilangan kuadrat adalah 81,karena 549162 – 81 = 549081.

2549162 741


L K S 6

c) Misal bil.yang dicari = a .5352 2 11 4 22a a a

Agar menjadi bilangan kuadrat makanilai 22x .

6. a) 236 6a a

b) 2( 3) 3a a

c) 2 24 4 (2 ) 2a a a a

d) 2 29 42 49 (3 7) 3 7a a a a


1. D8 3 24 4,899

1,6333 3 33

2. E

1 12 2

3 2 3 3 6 6 2,448 1,22462 3 3

3. A4 3 4 4 3 280 2 5 4 5a b a b a b b

4. B5 5 5 5 5 2 23 3 332 2 2 4x y x y xy x y

5. A1 1 1 13 3 3 3

1 13 3

3 333

22

6 (6 ) 2 6 212

4 2(2 ) 2mm m m

6. D3 3 2 612 12 122 2 2 4

7. C3 2 23 62 3 2 3 12

8. E3 3

3 3 6 2336

4 4 4x x y xyy

9. A123 8 3 3 8 4375 (3 5 ) 5 15k n k n kn k

10. B

55 5 152 2 4 3 7 3 744 3a a a a a a a


1. a.1 1 7

77

b.5

55

c.30 3

20 3 5220

d.6 1 1

48 38 28

e.8 2

147 7

f.6 2

2 63

2. a. 299 3 11 3 11

b. 5 2243 3 3 3 9 3

c. 61 1320 2 5 4 52 2

d. 2 2980 2 5 7 14 5

e. 24 12 4 2 3 8 3

f. 25 2 3 5 25 6

g. 5 31 1864 2 3 4 63 3

h. 2 22 2.000 2 2 5 10 40 5

3.

a. 4 2 4 298 2.7 7 2m m m

b. 5 3 5 2104 2 .13 2 26a b a b a ab

c. 2 5 2 2 5 2150 2.3.5 5 6x y x y xy y d.

3 5 8 4 3 5 8 2 4162 2.3 9 2m n y m n y mn y mn

e.5 12 2 5 12 2 6363 3.11 11 3ab c ab c b c ab

f. 5 8 2 5 5 8 2 2 496 2 .3 4 6x y z x y z x y z x

g. 6 12 4 6 12 3 481 3 9a b a b a b h.

1

5 2 8 6 5 2 8 2 2 2 23 33192 2 .3 4 3x y z x y z xz x y z


i.5 7 5

3 23 3

6 3 6 2

128 2 42

27 3 3m m m

mp p p

j.7 3 2 7 3

36 2 6 3

72 2 .3 22

9 3a a a

ab b b

4.

a. 3 2.3 6y y y

b. 3.2 23 64 4 16a a a

c. 3 2.3 64 4 4x x x

d. 4 4.2 86 6 6m m m

5.

a.3 3 3 34 4 4

44 2

6 6 6 2 24.4 22 22

m m m m

b.

6 6 6 3 3

23 3 3

64 2 8 3 8 3.

27 3 3 3 33

a a a b a bb b b b bb

c.

24 6 3 36 2 2 2333

24 33 4 4 23

3216 2 2 2 18.81 3 3 33 3

xyy y y xx x x xx x

d.

2 233 33

23 3

4 16.

4 44 4

y x yx xy yy y

e.

2233 35 5 5 2 23

4 3 32 4 2 223

3 32 4 2 2 2 2

22

332 2 2 2.

9 3 3 3

2 2 .3 2 1233

nm m m mn n n n n

m m n m m nnn n

f.2 4 24

42 2 24

81 3 3 2 3 2.

4 22 22

a a a b abb bb bb

g.5 88 2 2 2444

42 2 24

232 2 2 3 2 18.

9 33 33

yy y x y xx xx xx

h.

324 9 6 2 24 4 4

2 22 34 24

814 14 2 56 2 7 2.

8 88 8

nm m n mn n m nn n nn n

6.a.

246 46 3 138 1. 138

3 3 33 3

a b a b a a abab

a aa a

b.340 2 .5 13 2 130

.13 1313 13

a aa aa a

c.37 7 2 14.

8 42 2 2a a a a a

d.3

3 2

13 13 6 78.

54 183 6 6n n n m n mnm mm m m

e.3 6 2 336 3

.27 33 3 3

y y y xyy xx xx x

f.5 3 2 3 5 3 2

5 3 5 2

2

2

2

3

108 2 .3 6 327 3 3 3

2 .

2

a b a b a b abc c c c

a b ab cc c c

a b abcc

7.a.

222 2 525 4 20 25 2 5

54 4 4 2

yy y yy y

b. 22

23 4 3 4 316 9 24 16 33 8 .

3 3 33 3

x xx xx x

c.

22

2 4 1 4 1 21 16 8 1 28 4 .2 2 22 2

m mm mm m

d. 222

5 2 5 2 54 25 20 4 55 4 .

5 5 55 5

a aa aa a

8.

a. 5 2 cmb. 5 3 cmc.

2alas tinggi 5 2 5 25Luas = 2 cm

2 2 2

9.

a. 6 2. 3 2 3 1,41421 4,2432 2

b. 2 3 2 2. 3 1,73205 1,1553 33 3

c. 6 2 3. 2 6 2 2,44949 4,8993 3


L K S 7

d.

12 1 32 6

36 3

6 6 33

6 2,44949 1,732053

5, 476

e.2 1 3 6 3

. 1,39433 3

f.

1 1 1 5 3 25 3 25 3 2

6 5 10 3 15 230

1,732

10.

a. 2 2 2 26 3 27 3 3c b a

b. 2 2 2 213 6 133a b c

c. 2 2 2 22 3 13b a c

d. 2 2 2 212 8 208 4 13b a c

e. 2 2 2 220 10 300 10 3c b a

f. 2 2 2 240 25 975 5 39a b c


1.

a.4 5 6 15

2 2 2a b cs

2 2

4

15 7 5 3. . .2 2 2 2

3 .5 .7 15 72 4

L s s a s b s c

b.40 25 35 100 50 m

2 2s

4 2

2 2

50.10.25.15

3.5 .10

250 3 m 433,01 m

L

2.

7 19.3 253 4 23 7.5.3.2

59210

59.2 1210 210 119

x x x x x x

x x

x x

3.a.

2 5 27 5 7.5

735

5

1 1 1

1

1

x x x

x

x

b.

2 2 2.5 22 2 26 6.55

12230

225

1 1 1

1

1

a a a

a

a

4.

2 2 2

1 1 450 450002 40 0,04 40 4

2.3 .5 .10 150 2 15 2 2,6580 80 8

Tn

L m

5.40 2 22 2

980 7LTg


1. D

2 3 4 3 9 3

2. C

3 2 3 8a a


3. D

11 2 5 2 14 2

4. D

3 10 21 5 8 5

5. A3 1 3 77 74 5 8 40

6. E3 22 .3 2.2 2 7 2 6 2 4 2 7 2 3 2

7. E 25.3 3 3 3 10 3 3 3 15 3 10 9 3 13 3

8. A

7 3 4 3 3 3 7 4 3 3 6 3

9. E 2 2 2 5 2 1 2 5 2 2 2x x x x x

10. A 7 5 3 .5 5 5 7 15 5 23 5a a a a a a a


1.

a. 5 2 2 2 3 2 6 2

b. 3 3 5 3 4 3 2 3

c. 2.4 5 3 5 2.5 5 5

d. 2 7 3 7 5 7 10 7

e. 3.5 3 4.2 5 4 5 15 3 12 5

f. 2 6 2.6 6 5.3 6 5 6

g. 2 2 2.3 3 5.3 2 17 2 6 3

h. 9 2.2 6 5 3 9 4 2 3 5 3 9 3 4 2 5

2.a.3 3 3 3 3 3

3

3

2 .5 2 2.3 .5 5 2.5

2 5 6 10 25 10

2 5 31 10

a a a a

a a a a a

a a a

b.

2 3 5 2

2 2

2

2 .10 3 10 6 3 .10

2 10 3 10 18 10

5 10 18 10

10 5 18

a a a a

a a a a a

a a a

a a a

c.2 3 5 2 5

2 2 2

2

3 2.3 2 2

9 2 2 4 2

14 2

x x x x x

x x x x x x

x x

d.

2 3 4 2 5 2

2 2

4 6

4 6

2 2 3

a b a b

ab a a b a

ab a b a

e.

4 4 7 6 4 7

2 3 2 3

2 3

2 .3 2 .3

4 3 8 3

12 3

m n m n

m n n m n n

m n n

3.

a. 3 34 3 3 3 32 2.3 2 2 3 2 2

b. 3 34 3 4 3 3 33 2 .3 3 3 6 3 9 3

c. 3 34 3 3 3 37 3 2 2 .3 21 3 4 3 17 3

d.3 34 4 7 4 3 3

3

5 2 9 2 10 2 36 2

26 2

x x x x x x

x x

e.5 2 4 26 2 4 2.3 24 2 36 2

60 2

x x x x

x


L K S 8

f.

3 3 33 3 3 3 3 3

2 2 233 3

2 2 33

2 33

8 2 .3 4 2.3 3.5

16 3 12 2 5 3

11 3 12 2

11 3 12 2

m m m m m m

m m m

m m

m

4.

a.2 2 2

3 3 3a a a aa aa

b.3

22

2 3 2 9 112.3 2 2 2a a a a a

c.

2

2

3 3 12 3 3 122 2 2 2

3 3 122 2

a aa aa aa a a

aa a

d.

3 23 2 .3 16 3

18 3 2 3 3

18 3 2 3 3

16 1 3

x x xax x x

x x xxx x

x x x x xx x xx x

x

A. Evaluasi Pemahaman dan PenguasaaanMateri

1. B

3 3 3

2. D

6 6 6

3. B

3 6 3 2 3 3 2

4. A

7 7 2 7 2 7

5. B

8 6 2 2 2 2 3 2 4 6

6. B

2 8 2 3 16 2 6 4 2 6

7. D

3 2 3 2 3 4 1

8. A

6 1 6 1 6 1 5

9. C

7 5 7 5 7 5 2

10. B

23 1 3 2 3 1 4 2 3

11. C

212 2 12 2 24 2 14 4 6

12. A

2

4

10 8 10 2 8.10 8

18 2 2 .5

18 8 5

13. A

7 2 10

75; 2

10

Penyelesaian : 5 2

a b

a ba b

ab

14. B

8 2 15

85; 3

15

Penyelesaian : 5 3

a b

a ba b

ab


15. D

4.5 53 5 3 3 2

443

5 1;5

2 24

5 1Penyelesaian :

2 2

a b

a ba b

ab


1. a. 6 6

b.1 3 1 2 2 6 6 6 3 6

6 2 6 3 6

2 .2.3 2 .2 .3

2 .2 .3 108

c.61 3 1 2 2 6 3 6 2 3 62 .6 2 .6 2 .6 864

d.1 4 1 3 3 12 4 12 3 4123 .6 3 .6 3 .6

e.61 2 1 3 3 6 2 6 3 27 .5 7 .5 7 .5

f.101 5 1 2 2 10 5 10 2 57 .10 7 .10 7 .10

2. a. 21 5 3

b.

42 2 60 42 4 15 3 14 4 5

c.

42 2 .3 8 30 8 3 8 30 8 3 1 10

d. 21 14 15

e.

6 15 12 30 6 15 2 3 30

3 2 5 2 10

f.

2 7 21 2 2 6

7 2 3 2 2 3

2 3 7 2

g. 3 1 2

h. 7 5 2

i. 4.3 2 10

3. a.

6 2 60 10 16 4 15

b.425.8 20 80 40 240 20 2 .5

240 80 5

c.

36.3 84 3 49 157 84 3

d.

2

2

7 4 12 7 8 84 192

199 8 2 .21

199 16 21

e.

45 42 30 294 339 42 30

f.

16 35 4 42 4 30 6

4. a.

2 2 2 2x x y y

b.

2 2 1 1t t

c.

40 3 8 6 5 18 12

120 8 6 15 2 2 3

a a a

a a a


d.

28 7 16 70 6 70 12 100

56 16 70 6 70 120

8 7 2 70 6 70 120

m m mn mn

m m mn mn

m mn

5. a.

3 2 3 3

3 3 3 3 3

3 3 3

20 6 2 7 10 42

10 2 6 2 7 2 5 42

2 10 6 7 5 42

x x x

x x x x

x x

b.

5 2 5 5

55 5

16 7 8 4 2 28

2 8 7 4 4 28

x x x

x x

c.

4 4 4 4

4 4 4 4 4

6 40 12 96 14 30 28 72

2 2 3 20 6 48 7 15 14 36

d.3 3 3 3

3 3 3 33 6 6 9

3 3 3 3

3 3

54 160 9 40.32 6 48.4 48.32

54 2 .20 9 2 .20 6 2 .3 2 .3

108 20 36 20 12 3 8 3

144 20 20 3

6. a.

2

2

2 3

2 5 2 2 5 3 2 5

2 4 4 5 5 6 3 5

8 8 5 10 6 3 5

12 5 5

F x x x

F

b.

2

2

2

2 3

6 2 3 2 6 2 3 3 6 2 3

2 6 4 2.3 12 3 6 6 3

12 24 2 24 3 6 6 3

36 2 24 3 3 6 3

F x x x

F

7. a.

22

4

14 2 8 2 2

2

16 8 2 2 16 8 2 2

4 2 4 2

b.

Keliling 4 2 4 2 8 2 2 16 cm

c.

4

4

4 34

8 2 2 4 2Luas

2

32 2 8 2 22

16 2 4 2 cm

8. a.

15 2 5 2 2 5 2 5 5 2 5 2 5

30 15 5 2 4 5 5 4 5

30 15 5 2 5

27 15 5

b.

3

2

2

4.25 2 5 2 5

100 2 5 2 5 2 5

100 4 5 2 5

100 4 4 5 5

400 5 900

c.

3 22

3 322 2

5 2 5 2 5

5 4 5 5

9. a.

4 2 3

43; 1

3

Penyelesaian : 3 1

a b

a ba b

ab


b.

7 2 12

74; 3

12

Penyelesaian : 4 3 2 3

a b

a ba b

ab

c.

5 24 5 2 6

53; 2

6

Penyelesaian : 3 2

a b

a ba b

ab

d.

15 10 2 15 2 25.2

1510; 5

50

Penyelesaian : 10 5

a b

a ba b

ab

e.

21 215 21 5 4. 5 24 4

57 3;212 2

4

7 3Penyelesaian :2 2

a b

a ba b

ab

f.

9 4 4 2 3

4 2 3

43; 1

3

Penyelesaian : 4 2 3 3 1

9 4 3 1 9 4 3 4 13 4 3

13 2 4.3 13 2 12

1312; 1

12

Penyelesaian : 9 4 4 2 3 12 1 2 3 1

a b

a ba b

ab

a b

a ba b

ab

10.a.

2

2 3 5 2 3 5

2 3 5 2 3 5 2 3 5

2 2 6 3 5

2 6

b.

.

5 2 6

53; 2

6


7 2 12

74; 3

12

Penyelesaian : 7 2 12 4 3 2 3

6 2 8

64; 2

8


5 2 6 7 2 12 6

a b

a ba b

ab

a b

a ba b

ab

a b

a ba b

ab

2 8

3 2 2 3 2 2

2 3 2 2


1. a.

2

22

2 2 2

2

x y z

x y z x y z

x y xy xz yz z

x y z xy xz yz

b.

5 3 2

5 3 2 2 5.3 5.2 3.2

10 60 40 24


L K S 9

2.

30 10 5 30 2 25.5

3025; 5

125

Penyelesaian : 25 5 5 5

x y

x yx y

xy

a b

Jadi, 5; 5a b

3.

48 2 12

3 ; 3

....(1)

12......(2)

Substitusi 3 ke (2) :

3 12 4 4 2

Substitusi 4 dan 3 ke (1) :

4 3 7 7

a a

b x y b x y

x y a

xy

y

x x b

x y

a

4. a.

4

4

4

27 8 11 27 2 176

27 2 176

2716; 11

176


Jadi, 27 8 11 4 11

27 8 11 27 2 176

27 2 176

2716; 11

176


i a b

a b

a ba b

ab

ii a b

a b

a ba b

ab

4

4 4

1

Jadi, 27 8 11 4 11

27 8 11 27 8 11

4 11 4 11

b.

155 5

15

2 3. 2 3 2 3 2 3

4 3 1

c.

1 1

361 19219 8 3 19 8 3

1 113169

5. a.

2 24 4a b a b a b a b

a b

b.

133 3

13

20 14 2. 20 14 2 20 14 2 20 14 2

400 392 2


1. C

337 81 7 7 21

27 .32 3 2 2 2

2. A

4 3 5 215

52 5 5

3. B

24 2 6 1 17

7168 2 42 7

4. B

24 54 150 2 6 3 6 5 60

4 6 4 6

5. D

28 8

4 27 57 5 7 5

6. B

14 35 14.35 14.35 49 715.24 36 615 24 15.24


L K S 107. E

42 15 14.35 42.15 9 3 7 37

35.56 28 1435 56 15.24 2 7 7

8. A

27 2 162

2718; 9

162

Penyelesaian : 27 2 162 18 9 3 2 3

33 800 33 2 200

3325; 8

200

Penyelesaian : 33 800 25 8 5 2 2

27 2 162 33 800

3 2 3 5 2 2

2 8

a b

a ba b

ab

a b

a ba b

ab

9. C

25 2 126

2518; 7

126

Penyelesaian : 25 2 126 18 7 3 2 7

19 336 19 2 84

1912; 7

84

Penyelesaian : 19 336 12 7 2 3 7

25 2 126 19 3362 3 3 2

3 2 7 2 3 7

2 3 3 2

3 2 2 3

2 3 3 2

a b

a ba b

ab

a b

a ba b

ab

1

10. D

48 216.2 4 2

3


1. D

1 9 8 9 8. 3 2 29 89 8 9 8

2. A

7 3 2 21 7 2 21 7 2.9 2 73 2 3 2

3 2 3 1, 4142

1,5858

3. D

1 3 2 3 2. 3 2

3 23 2 3 21,732 1, 414

0,318

4. C

4 2 4 3 2 3 8 4 6 4 6 12. 2

2 2 2 3 2 3 4 2 6 2 6 6

5. C

4 2 2 1 4 2 4 2 2.

2 12 1 2 1

3 2 2 3 1, 4142 2

2,2426

6. B

2 1 2 1 2 2 2 1. 3 2 22 12 1 2 1

3 2 1, 4142

0,4142

7. E

2 27 5 7 5 7 2 35 5 7 2 35 5 12

7 5 2


8. D

8 7 9 8 6 5 7 6 1

55 49 8 8 7 7 6 6 5

9. D

13 5 2 3 5 13 2 39.

25 4.35 2 3 5 2 3

5 13 2 3 1313

135 2 3

13

10. D

1 3 1 3 1 3 1 3 1 3 1 3 1 3

1 31 3 1 3

2 2 32

1 3

11. A

2

2 3 5 2 2 3 102 .2 3 5 2 3 5 2 3 5

2 6 102 2 6 3 52 6 10 6

.2 6 6

2 6 6 2 1512

3 6 156

12. B

2

2 3 76 2 6 18 42.

2 3 7 2 3 7 2 3 7

2 6 3 2 424 4 3 3 7

2 6 3 2 42 3.4 3 3

2 18 3 6 42.312

6 2 3 6 3 1412

1 2 2 6 144

13.

2

2 3 55 3 2 .2 3 5 2 3 5

5 3 2 3 5 5 3 2 2 3 10

2 3 5

10 15 6 3 5 15 2 6 10

2 2 6 3 5

2 15 3 6 2 90 3 6 6 10 3 6 2 10 6.

12 12 42 6 6

14. A8 3 3 5 4 3 4 5 32.3 32 15 12 15 12.5

.16.3 16.54 3 4 5 4 3 4 5

96 20 15 6032

36 20 1532

9 5 158

15.

2

5 3 25 10 15 6 .5 3 2 5 3 2

5 5 5 3 5 2 50 30 20 15.5 15.3 30 30 18 12

5 3 2

5 5 5 3 30 2 5 5 3 3 5 3 2 2 35 2 15 3 2

3 2 8 3 6 5 306 2 15


1.a.

1 5 3 5 3 1. 5 35 3 25 3 5 3

12, 23607 1,73205 0, 25201

2

b.

3 2 1 6 3. 6 3

2 12 1 2 12, 44949 1,73205

0,71744


c.

2 3 2 2 6 4 2. 6 4 2

9 83 2 2 3 2 26 4 1, 41421

0,34316

d.

5 2 3 2 10 3 10 10 3 10.

12 4 82 3 2 2 3 25

3 145

1,73205 1 3, 41506254

e.

2 2 1 2 2 1 8 2 2 2 2 1 9 4 2.

8 1 72 2 1 2 2 19 4 1,41421

72,0938

f.

3 1 2 3 2 3 3 2 3 32 3 2 3 3 3 3 52 3 3 1

2 1,73205 33 1,73205 5

6, 464110,196150,6339

2.a.

3 2 6 3 12 2 3 13 3 2 3 2 6 3 12 2 3

b.

2 3 2 3 3 6 3 2 3 2. 39 3 33 3 3 3

3.a.

1 2 3 2 3. 2 3

4 32 3 2 3

b.

2 1 2 1 2 2 2 1. 3 2 22 12 1 2 1

c.

1 3 2 2 3 2 2. 3 2 2

9 83 2 2 3 2 2

d.

4 5 1 4 5 4. 5 1

5 15 1 5 1

e.3 2 7 13 6 7 3 13

.28 132 7 13 2 7 13

2 7 135

f.

4 3 1 3 2 4 12 6 12 2 16 3 16.18 163 2 4 3 2 4

6 6 6 2 8 3 8

g.

2 4 7 2 7 1 4 7 56 2 4 7. 2

28 12 7 1 2 7 1

h.

3 1 2 3 3

2 3 3 2 32 3 3 1

3 3 1 3 3 3.

23 1 3 1

i.

3 2 6 3 3 12 3 6. 12 66 36 3 6 3

6 3 2 18 12. 18 123 23 2 3 2

3 2 612 6 18 12

6 3 3 2

2 12 6 18

4 3 6 3 2


j.

3 2 6 3 3 12 3 6. 12 66 36 3 6 3

4 3 6 2 4 18 4 6. 18 6

6 26 2 6 2

6 3 2 18 12. 18 12

3 23 2 3 2

3 2 4 3 66 3 6 2 3 2

12 6 18 6 18 12 0

4.a.

47 6 10 47 2 90

4745; 2

90


10 10 34 5 3 2 10 50 34 5 30 20 102 2.

5 185 3 2 5 3 2

50 2 34 5 60 5 102 213

52 2 26 5 4 2 2 513

25 5. 5 5

5 5

10 10 34 147 6 10 2555 3 2

45 2 4 2 2 5 5 5

3 5

a b

a ba b

ab

5 2 3 5 5 2

b.

3 2 2

32; 1

2


2 1 2 2 1 4 2 2 2 1.

8 12 2 1 2 2 1

5 3 27

18 8 2 18 2 3218

16; 232


22 2 24 2

a b

a ba b

ab

a ba b

a bab

2 1 4 2.

4 2 4 21

4 2 4 2 22

16 21

3 2 2 12 3 2 214 281 1

22 1 2 22 3 2 2 18 8 2

5 3 2 13 2 2

7 2820 12 2 3 2 2 18 15 2

28 28

5. a.

3 2

3 2

2

3 1 3 1 3 14 2 8 7

2 2 2

1 13 1 3 1 4 3 1 72 21 1

6 3 10 2 3 4 4 3 4 72 23 3 5 3 2 4 3 3 10


L K S 11

b.

2 2

2 2

3 2 3 2 3 2 3 23 2 3 2 3 2 3 2

3 2 6 2 3 2 3 2 6 23 23 2 6 2 3 2 6 2

5 2 6 5 2 61

5 2 6 5 2 6

5 2 6 25 24 5 2 6

25 24

25 20 6 24 1 25 20 6 24 99


1.

2 2

.a x a x a x a xa x a x a x a x

a x a x a x a x a x a x

a x a x

a a xx

2.

2 2

2 2 3 61.

2 2 3 6 2 2 3 6

2 2 3 6

2 2 3 6

2 2 3 6

4 4 2 2 3 2 18 6

2 2 3 63 4 2 6 2

2 2 3 6 2 2 3.

2 2 3 2 2 3

4 2 4 2 6 2 12 6 3 2 3 3 3 68 9

2 2 6 32 2 6 3

1

4.

7 7 1

29 7 9 716 2 63 16 2 63

5.

3 3

3 33 3

7 5 7 57 5 7 5

7 5 7 5 7 2 35 5. 6 357 57 5 7 5

7 5 7 5 7 2 35 5. 6 357 57 5 7 5

7 5 7 5 6 35 6 357 5 7 5

216 108 35 630 35 3 216 108 35 630 35 31692

Soal Khusus untuk Penggemar Matematika

1.

33 33 3 5a b a a b a b


1. B2 3log8 3 8 2

2. C33 log x y y x

3. Blog a cb c b a

4. Dlog x aa b b x

5. B4 4 3log 64 log 4 3

6. A5 5 4log 625 log5 4

7. Alog100.000 5

8. A0,1 log100 100 (0,1) m

2 1 210 (10 ) 10 10 2 m m m9. B

5 5 3log125 log5 3 b b b3 3 3log 27 log 27 log3 3 b

10. B8 log8 1


L K S 12


1. a) 3216log6 b) 481log3

c) 481log3

1

d) 327log3

1

e)43

81log16

f) 239,7log e

g)329log27

h)43

271log81

i) 305,0log e

j)31

51log125

2. a) 2733 b) 12827 c) 21663

d) 4934332

e)361

6 2

f)49

278 3

2

g) 1,20ln3 h) 72,2ln i) 41,148ln 5

j)827

8116 4

3

3. a) 642 x

622 x

6xb) 51283 x

c)9

162 x

43

43

22

x

x

d) 81010 x

8xe) xee 6

6x

f) 421

x

2

21

21

x

2xg) 33 12 x

3xh) 4ee x

4x

i) 2

1e

e x

2ee x

2xj) 310 xee

103 x7x


1. E2 2log( ) log( )( )

= log( ) log( )

a b a b a b

a b a b2. B

33 21log log log log xx x

x x3. A

2 2 2 2 4 12log 4 log12 log 6 log6

2 2 3log8 log 2 3


4. D

6 365100 100

4

5

4

6 36log log log 4 5 log 54100 100

1log 5 log log104 54 10

10log log1010

5. D2

2 2 2 2

Diket: log3 1,585

log 6 log 2 3 log 2 log3 1 1,585

6. D

log log log log p qa a a aq pp

q

pqpq pq

2log 2 log a aq q7. D

log log log a a abc b

c

bcbc

2log 2 log a ac c8. A

log10 log100 log1.000 log10.000log100.000 1 2 3 4 5 15

9. D11 145 311 14 22

5 3 15 2215

log log log log log 7

10. A3 55 363 5 1

5 36 12 112

log log log log log1 0

11. C

13

13

2

log125 2log 4 log32

log125 log 4 log325 32log5 log16 log32 log log10 1

16

12. Dlog log log

1010

z

z

x y z xy z

xy xy

13. A2 2 2

2 2 2

log log log

log log1 0

a b cbc ac ab

a b cbc ac ab

14. A1,9675Diket:log 1,9675 10

log(1.000 ) log1.000 log3 1,9675 4,9675

x xx x

15.

2 2

Diket:log 2 , log3 , log5

log150 log 2 3 5 log 2 log3 log52

a b c

a b c


1. a) 8log16log 22 )2.2.2log()2.2.2.2log( 22

2log2log2log2log 2222 2log2log2log 222

2log7 271.7

b) 16log64log4log 222 2log42log6)2log(2 222

4462 c) 16log246log 44

)4log(2)4log(4 44 224

d) 3log27log81log 333 )3log(8 3

81.8

2. a)

96

log3

log22 xx

xx

x

b)

3

3

1log

yx

c)

31log1

31log 2

1

3

xxx

xx

d) )3log(13log 232 xxxx

e)

2

3

3

3

3logloglog

yxz

yxxz

zx

yx

f)

32

32

logyabx


3.a) rqp logloglog b) baaba log).log(loglog 2

baa logloglog ba loglog2

c) ).log(logloglog 2 bbaba bba logloglog

ba log2log d)

baaaba logloglog2)log(log 2 ba loglog

e) baba loglog2loglog 2 f) baba log2log3loglog 23 g) aaa loglog0log1log h) )log(log1log 22 abaaba

4. a) )3.2.2log(3log2log2log

3log2log2 4771,0)3010,0(2

0791,1b) 2log10log)2.10log(

3010,12log1 c) 3log10log)3.10log(

= 4771.13log1 d) = 3log2log10log)3.2.10log(

7781,2

e) 2

1

2log3log)2.3log(

6276,02log213log

f) 3log100log)3.100log( 3log)10.10log(

3log10log2 4771,2

g) 2log)10.10.10log()2.1000log( 2log10log3

3010,3

h)

103.2log

106log

10log3log2log 2219,0

i)

10.10.102log

10002log

10log32log 699,2

j)

23.3log

29log

2log3log2 6532,0

5.

a)

185.18.2log

3.65.18.2log

)5.2log(110log

b)

7720720log

710

.4,14.5

10.9.8log 77

17log7

6.

a)

5log

5log

3

2

1

3

xxy

x

xy

b)

23

2

2 3log

)3(1log

yyxx

yyxx

c)

yyyyy

31log

33log 22

d)

9

393 1loglog1log

xxxx

7.a) 398,03010,06990,02log5log b) 4771,0)6990,0(23log5log5log

= 1,8751c) log 75 – log 4 = 1,8751 – log 2 – log 2

= 1,8751 – 2(log 2)= 1,8751 – 2(0,3010)= 1,2731

d) log 3 + log 3 + log 3 + log 3 – log 5 – log 5= 4(log 3) – 2(log5)= 4(0,4771) – 2(0,6990)= 0,5104

e) log (100.2) = log 100 + log 2= 2 + 0,3010= 2,3010

f) log 2 + log 2 + log 2 + log 2 – log 3= 4 (log 2) – log 3 = 4(0,3010) – 0,4771

= 0,7269


L K S 13

8.

qp

pq

p

p

p

x

x

xx

x

x

4log

4log

3log4log

)3.4log(

12log

4loglog4

log xxx xx

qpqp

1)(1

9. a)

10.a)

2100

1log10099.

9998........

43.

32.

21log

b)

3216

1log

216215

.215214

........43

.32

.21

log 66


1. A2 5 2 5 4log( log 625) log( log5 )

2 2 2log 4 log 2 4 2.

13 4 11

3log81 81 3 (3 )

4

m mm

m

3. C

2

2

2 3

6 3

6

3

log1.728 1.728 (2 3)

2 3 2 3

2 2 66

3 3 6

m

m

m

m

m

m

mm

m

4. B2 2 2 2

2 2 2 2 16 2 2 2

2 2 2 0

log log log log 65.536

log log log log 2 log log log16

log log 4 log 2 1 2

5. E

10

1

10 10

log log log 1 log log 10

log 10 10

x x

x x6. A

2 3 2 3 2 1

2 2 9

log log log 1 log log 2

log 3 2 512

x x

x x7. B

2

1

25 25 5 512

10log 2 1 2 10 52

log log5 log5 log5 0,5

x x x

x

8. C13

433

8 6 3 5

2 6 3 3 4 5

1 43 3

log 2 log 216 log81 log(625)

log 2 log 6 log3 log5

3 4 0

9. C

3 12 2

3 512 2 2

2

2

2

log log loglog

log log loglog

log log( ) 5log log 2

y y x x yxy

y x x yxy

y x x y xyxy xy

10. BDiket: 0,909090... dan 1,331100 90,909090...

0,909090...

a baa

______________ _90 1099 1199 90 a a

3

3 3

31110 3 310

11

31

1,331 1.331 1.000 11 101 1

log log log 3

a a aa

b

a

b a

12. B

3 32

3 32

Diket: log1,5 ; log3

log1,5 log1,5loglog

diperoleh:log3 log3loglog

log1,5 log3 log

33 log2

n n

ab

x

a b

a nn a

b nn b

aa b xbx


13.

1 14 4

2 2 24

4 4 4 4

22 2

2 24

1log 4 10

10

1 10010

100 1log log log

2

a a a

b b b

a b ab

b b aa a a

14. E5

5 2 5 5 2

Diket: log3

log 75 log3 5 log 3 log5 2

a

a15. C

1 13 3

2 2 2 23 3 3 2 3 3

3 3 3 3

2 23 3 3

3 31 1 13 3 3

log 45 log5 log3 log5 log5

log 15 log3 log5

2 log 5 log5 4(1 log5)12

log5 (1 log5)


1.a) 83log.83log)3log( 383243 b) 122log.122log)2log( 2122342 c) 212log.212log)2.2log( 22123522

d) 43log.43log)3log( 34321

83

e)27

3log.27

3log)3log( 327

3273

f) 14log44

log 4

2

2

34

g)32

2log.32

2log22

log 232

231

4

62

h.25

2log.25

2log)2.2log( 225

223

42

2.

a) 21

15log = 35log21

= 3log5log21

= 0,58805b) 2log23loglog5log 2

= 2 log 5 + log 3 – 2 log2= 0,2731

c) 4 log 3 – 2 log 5 = 0,5104

d) 4515,02log.23

e)21

(2 log 10 + log 2) = 1,1505

f)21

( 2 log 2 + 2 log 3) = 0,7781

3.a)

b) a = 0,636363100a = 63, 6363

a – 100a = -63-99a = -63

a =117

9963

117

loglog2

4923

2 ab

117

log49121

21

117

log

2

117

4.

9log1575log.4log

21575log4log343

43

9log1575log 33

175log9

1575log 33

7.25log3 7.25log4log 43

7log25log4log 443

7log5log4log

1

41

243

7log5log.24log 4

143

cab 2


L K S 14


1. C

2 3

2

1 1 log 2 log3log36 log36log36 log36

log 2 log3 log 6 log 6 1log36 log36 2log 6

2. C

2 51 1 log 2 log 5

log100 log100log100 log100log10 1log100 2

3. D4 3

44 3 4

3

4 4 4 4

Diket: log3 dan log5

log3log3 log5 log5

log5

log15 log3 5 log3 log5(1 )

a b

aab

b

a ab a b4. E

4 log 39 ada di antara 5 dan 6.5. B

20 64

12

1 1log 25log10 log100log 20 log 64log 25log10 log100

log 25 log 20 log 64

25 8log log10 120

6. A

5 2

5 5 3 515

5 5 5

15

5

Diket: log3 dan log5 .

log 40 log 2 log5log 40

log15 log3 log5

3 13 log 2 1 31 ( 1)log 3 1

b

a b

ba b a

7. B

3 4 51 1 1

log 60 log 60 log 60log3 log 4 log5

log 60 log 60 log 60log3 4 5 log 60 1

log 60 log 60

8. A3 4 5 6 7 8

3 2

log 4 log5 log 6 log 7 log8 log9

log 3 2

9. A1 1 1

log 1 log 1 log 11 1 1

log log log log log log1 1 1

log log loglog log log log

1log log log log

a b c

a a b b c c

a b c

bc ac ab

bc a ac b ab c

abc abc abca b c abc

abc abc abc abc

10. C

2

1 1 1log( ) log( ) log( )

log log log log( ) 2log( ) log( ) log( ) log( )

xy yz xzxyz xyz xyz

xy yz xz xyzxyz xyz xyz xyz

11. B

7

7 2

2 2 298

2 2 2 2

21log 2

Diket: log 2 dan log3

log 6 log 2 log3log 6log98 log 2 log 7

1 1 ( 1)1 21 2

a

a b

b b a ba

12. B

3

3

2

2

log2 3 3log 2

2 3 3loglog 2

log3 2 2log3

3 2 2loglog3

log log 3log log3log loglog log

log log 2log log2log loglog log

Jadi, .

a

b

a

b

a a a amb bb b

a a a anb bb b

m n

13. B225 5 3 53

2

5 32 33 2

log 27 log3 log3

log3 log5

aa

a a a

14. D

1 1 1

1 1 1

log log log

log log log

( 1) log ( 1) log ( 1) log

log 1

a b cb c a

a b c

a b c

a

b c a

b c a

a15.

1 1 1

log log log

log log loglog log10

log log log log log

p q rq r p

p p qq r rq p q r pr

x x x

x x x x x



1.a)

2.

22log88log88log 3

322

2log11log8log11log

33

33

2log11log2log11log

33

333

2log11log2log.311log

33

33

abab

3

3.

4

202128220210log2

4log4

16log 22

42log 22 21

4.a)

5.

a)6log

2log.6log.3log5

3532

36log6log.3

6log6log.3log.2log.3

5

5

5

325

b)

81

log

251

log

81

log

1004

log

2

5

2

5

32

25

2log5log

32

25

2log

5log21

31

62

c)

21

log2log3log9log22 33222

13322 2log2log3log9log2

2log

21

2log39

log3

32

2log

21

3log3

2

21

2log.3log.21 32

d) 4333222 2log2log3log27log22

= 2log22log.33log27log 3322

2log3.27log 32

2log3log 34242log.3log.4 32

6.a) log 6 = log (2.3)

= log 2 + log3= a + b

b) log 600 = log (100.6)= log 100 + log 6= 2 + a + b

c) log 5 = log (10:2)= log 10 – log 2= 1 – a

d) log

151

= log 1 – log 15

= log 1 – log (5.3)= log 1 – log 5 – log 3= 0 – (1-a) – b= a – b – 1

e) log 0,75 = log

10075

= log

43

= log 3 – log 4= log 3 – ( log (2.2))= log 3 – log 2 – log 2= log 3 – 2 log 2= b – 2a


f) log 30 = log 21

30

=21

log (10.3)

=21

(log 10 + log 3)

=21

(1 + b)

g) 2.6log12log 22 2log6log 22

= 12log6log

1

a

ba

aba

2

h) 2

1

321

91

1005

log05,0log2

1005log.

41 3

3log100

5log

.41

3log100log5log.

41

ba 21.

41

ba 2.

41

i)

45log25,1log 66

4log5log 66 2log.25log 66

6log2log.2

6log5log

6log

2log25log

baa

baaa

3121

7.a)

24624

62

logloglogloglog zyxazyxa aaaaa

zyxa aaaa log2log4log6log2 = 2.1 + 6.p – 4.q – 2.r= 2 + 6p – 4q – 2r= 2 ( 1 + 3p – 2q – r)

b)

4

121

log zxya

zyx aaa log.41

log.21

log

rqp41

21

c)xy

zyz a

aaxa

loglog

loglog.log

prq

8.

a) a23

2log1

3

b)aa 4

923

.23

3log.23 2

c) aa 232

.32log.3 3

10.

a) 2log3log23log 222

= 13log2

d) 5,1.25log4

23

.4

100log4

23

.4log100log 44

23

14log

100log

= ( log 100 – log 4 – 1) .23

= ( 2 – log 4 – 1 )23

= ( 1 – log 4)23


L K S 15C. Evaluasi Kemampuan Analisis

1. 100xyz xyz210 2log xyz ..... (1)

43

loglog

yx

yx log4

3log

... (2)

54

loglog

zy

yz log45log ... (3)

log (xyz) = log x + log y + log z = 2

Substitusi: ylog4

3

+ log y ylog45 = 2

3 log y = 2

32

log y 32

10y

Substitusi32

log y ke (2), didapat 21

10

x

Substitusi32

log y ke (3), didapat 6

5

10

z

2.

3.6264 xa 6log2 xa 6log.2 ax

6264 yb 6log2 yb 6log.2 by

6264 zc 6log2 zc 6log.2 cz

6logloglog 222 cba

6666

zyx 1

111

zyx


1. B(Berdasarkan sifat logaritma)

2. C

532log

535

= 55

35 32log

53

32

353

5 22 3. E

3 5log23

323 5log

254. B

3223 2log

32log3

12

5. B

5 81log215

5 81log5

= 9

6. A

7. B

5log2

2 5log2

2

58. A

3232

33

42 21log

3log

2411

8032

81

81

9. E10. D

1629 42log 54

59


2.

a) 32

13 9log

9

1


U K A B 1

b) 2 54

log2

54

c) 25225log2

d) 588,558log8,5

e)

8332 2.121log

= 32

332 2.121log

=

23332 2.121log

= 333 2.121= ( 121 . 2 ) = 242

f) 1010)log(loglog mnnm

= mn.

A. Pilihan Ganda

1. B

2

42

2

3

24

618

bb

abaa

222 523 ababab 2. C

43

61

43

32

21

133

3. B4. B6. D

3161952 33 n

2n + 5 + 9 – 1 – 16 = 32n = 6

n = 37. E

23

425

33

23

425

58. C9. D10. A

54

5

5

23

= 4

4

23

8116

32

4

4

11. C12. B

03,0100

3103 2

1

4

2

13. B

3.52351528

35 14. C

3.43.253.92 323536

3315. C16. C17. D18. D

24 232423

43

32

21

xxx

19. E

3.723721210

37 20. B

2.11221122213

21121. A22. B

33232

1232.

331

3333

33232

3323

64

24. B25. D28. D29. B30. E31. D33. B36. B

101loglog2log

log2

log

222

22

aa

aa


37. D

4log2log4log 2

22log 22

38. B

B. Bentuk Uraian

1.23

5

a

223

52

22

a

2625

25

625625

6256435

650127 2. a)

2101674210474

1460

146021460

840274

3. a) 3ab – 2bc + abc

52525

525225253

)1(5)1(25215

5593

51527

5251530

b) 221

3 . bca

221

3 52525

1125

15

)54(5

23

22

3

4. b)

2100log35137

260

log

3513

115

74143

log

3513

115

74

20449log

115

log3513

log74

log20449log 21

5. a)

42log56log56log 3

342

13

11

33log2log7log

2log37log

6log7log2log7log

67log87log

333

33

33

333

3

3

aabab

ab

ab

b)

66log44log44log 3

366

12

11

23log2log11log

2log211log

)6.11log(4.11log

333

23

3

3

aacac

ac

ac

Documents

BAB 1 Bentuk Pangkat, Akar, Dan Logaritma