bab 1 bentuk pangkat, akar, dan logaritma
DESCRIPTION
Kunci SUKINO 1A Bab 1TRANSCRIPT
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
Kunci Penyelesaian Matematika SMA Jl.1A – Sukino Bab 1 | page 2
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
Kunci Penyelesaian Matematika SMA Jl.1A – Sukino Bab 1 | page 3
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
B. Evaluasi Pemahaman dan PenguasaanMateri
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
Kunci Penyelesaian Matematika SMA Jl.1A – Sukino Bab 1 | page 4
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
A. Evaluasi Pengertian atau Ingatan
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
Kunci Penyelesaian Matematika SMA Jl.1A – Sukino Bab 1 | page 5
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.
B. Evaluasi Pemahaman dan PenguasaanMateri
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
Kunci Penyelesaian Matematika SMA Jl.1A – Sukino Bab 1 | page 6
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
C. Evaluasi Kemampuan Analisis
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
Kunci Penyelesaian Matematika SMA Jl.1A – Sukino Bab 1 | page 7
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
A. Evaluasi Pengertian atau Ingatan
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
Kunci Penyelesaian Matematika SMA Jl.1A – Sukino Bab 1 | page 8
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
B. Evaluasi Pemahaman dan PenguasaanMateri
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
Kunci Penyelesaian Matematika SMA Jl.1A – Sukino Bab 1 | page 9
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
Kunci Penyelesaian Matematika SMA Jl.1A – Sukino Bab 1 | page 10
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
C. Evaluasi Kemampuan Analisis
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
Kunci Penyelesaian Matematika SMA Jl.1A – Sukino Bab 1 | page 11
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 .
A. Evaluasi Pengertian atau Ingatan
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
Kunci Penyelesaian Matematika SMA Jl.1A – Sukino Bab 1 | page 12
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
B. Evaluasi Pemahaman dan PenguasaanMateri
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
Kunci Penyelesaian Matematika SMA Jl.1A – Sukino Bab 1 | page 13
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
A. Evaluasi Pengertian atau Ingatan
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
B. Evaluasi Pemahaman dan PenguasaanMateri
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
Kunci Penyelesaian Matematika SMA Jl.1A – Sukino Bab 1 | page 14
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
Kunci Penyelesaian Matematika SMA Jl.1A – Sukino Bab 1 | page 15
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
C. Evaluasi Kemampuan Analisis
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
A. Evaluasi Pengertian atau Ingatan
1. D
2 3 4 3 9 3
2. C
3 2 3 8a a
Kunci Penyelesaian Matematika SMA Jl.1A – Sukino Bab 1 | page 16
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
B. Evaluasi Pemahaman dan PenguasaanMateri
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
Kunci Penyelesaian Matematika SMA Jl.1A – Sukino Bab 1 | page 17
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
Kunci Penyelesaian Matematika SMA Jl.1A – Sukino Bab 1 | page 18
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
B. Evaluasi Pemahaman dan PenguasaanMateri
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
Kunci Penyelesaian Matematika SMA Jl.1A – Sukino Bab 1 | page 19
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
Kunci Penyelesaian Matematika SMA Jl.1A – Sukino Bab 1 | page 20
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
Penyelesaian : 5 2 6 3 2
7 2 12
74; 3
12
Penyelesaian : 7 2 12 4 3 2 3
6 2 8
64; 2
8
Penyelesaian : 6 2 8 4 2 2 2
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
C. Evaluasi Kemampuan Analisis
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
Kunci Penyelesaian Matematika SMA Jl.1A – Sukino Bab 1 | page 21
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
Penyelesaian : 27 2 176 4 11
Jadi, 27 8 11 4 11
27 8 11 27 2 176
27 2 176
2716; 11
176
Penyelesaian : 27 2 176 4 1
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
A. Evaluasi Pemahaman dan PenguasaaanMateri
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
Kunci Penyelesaian Matematika SMA Jl.1A – Sukino Bab 1 | page 22
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
A. Evaluasi Pemahaman dan PenguasaaanMateri
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
Kunci Penyelesaian Matematika SMA Jl.1A – Sukino Bab 1 | page 23
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
B. Evaluasi Pemahaman dan PenguasaanMateri
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
Kunci Penyelesaian Matematika SMA Jl.1A – Sukino Bab 1 | page 24
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
Kunci Penyelesaian Matematika SMA Jl.1A – Sukino Bab 1 | page 25
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
Penyelesaian : 47 6 10 45 2
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
Penyelesaian : 3 2 2 2 1
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
Penyelesaian : 18 8 2 4 21 1 1
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
Kunci Penyelesaian Matematika SMA Jl.1A – Sukino Bab 1 | page 26
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
C. Evaluasi Kemampuan Analisis
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
A. Evaluasi Pengertian atau Ingatan
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
Kunci Penyelesaian Matematika SMA Jl.1A – Sukino Bab 1 | page 27
L K S 12
B. Evaluasi Pemahaman dan PenguasaanMateri
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
A. Evaluasi Pengertian atau Ingatan
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
Kunci Penyelesaian Matematika SMA Jl.1A – Sukino Bab 1 | page 28
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
B. Evaluasi Pemahaman dan PenguasaanMateri
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
Kunci Penyelesaian Matematika SMA Jl.1A – Sukino Bab 1 | page 29
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
Kunci Penyelesaian Matematika SMA Jl.1A – Sukino Bab 1 | page 30
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
A. Evaluasi Pengertian atau Ingatan
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
Kunci Penyelesaian Matematika SMA Jl.1A – Sukino Bab 1 | page 31
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)
B. Evaluasi Pemahaman dan PenguasaanMateri
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
Kunci Penyelesaian Matematika SMA Jl.1A – Sukino Bab 1 | page 32
L K S 14
A. Evaluasi Pengertian atau Ingatan
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
Kunci Penyelesaian Matematika SMA Jl.1A – Sukino Bab 1 | page 33
B. Evaluasi Pemahaman dan PenguasaanMateri
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
Kunci Penyelesaian Matematika SMA Jl.1A – Sukino Bab 1 | page 34
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
Kunci Penyelesaian Matematika SMA Jl.1A – Sukino Bab 1 | page 35
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
A. Evaluasi Pengertian atau Ingatan
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
B. Evaluasi Pemahaman dan PenguasaanMateri
2.
a) 32
13 9log
9
1
Kunci Penyelesaian Matematika SMA Jl.1A – Sukino Bab 1 | page 36
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
Kunci Penyelesaian Matematika SMA Jl.1A – Sukino Bab 1 | page 37
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