PEMBAHASAN LOGARITMA KELAS X
PEMBAHASAN LOGARITMA
PEMBAHASAN
1. Jawab : D
Ingat :
a
5
x=a n
log x=n ↔
log 25 = 2
↔
25=5
2
2. Jawab : A
Ingat :
2
a
log x=n ↔
x=a
log 32 = 2p
n
↔ 32 =
2
2p
3. Jawab : A
Ingat :
a
x=a n
log x=n ↔
7-2 =
1
49
log
7
↔
1
49
= -2
4. Jawab : E
2
4 ×10
5
log 4 + 2log 10 – 2log 5 = 2log
= 2log 8
= 2log 23
= 32log 2 = 3
× 1=3
5. Jawab : B
2
48
3
log 48 – 2log 3 = 2log
= 2log 16
= 2log
4
2
= 42log 2 = 4
× 1=4
6. Jawab : C
5
log 50 – 5log 2 = 5log
50
2
= 5log 25
= 5log
52
= 2 5log 5 = 2
× 1=2
7. Jawab : E
1
8
log ( 64 x × 4 )
=
8
log ( 64 x × 4 )
= 8log
64 x × 4
2
x
8
3− x
83− x
=
26 x ×22=
6x
3−x
83
8x
3
2 ×2 × 8 =8
26 x ×22 × 23 x =2 9
2
9 x +2
=2
9
=9
9 x+ 2
9 x=7
x=
7
9
8. Jawab : B
6
log 15 = 6log 3 . 3log 15
1
❑
=
. 3log 3 . 5
=
1
❑
. 3log 3 + 3log 5
=
1
❑
.
1+b
1
1+
a
=
(1+b)
=
1+b
a+1
a
=
(1+b ) a
a+1
9. Jawab : D
3
log 36 + 5log 100 – 3log 4 – 5log 4 = 3log 36 – 3log 4 + 5log 100 – 5log 4
= 3log
36
4
+ 5log
100
4
= 3log 9 + 5log 25
= 3log 32 + 5log 52
=2+2=4
10.
Jawab : A
b3
log
a
2
=
=
2
3
.blog a
2 1
2
. =
3 p 3p
2
11.
Jawab : E
2x = 18
2
log 18 = 2log 2.9 = 2log 2 + 2log 9
= 2log 2 + 2log 32
= 1 + 2 2log 3
12.
4
Jawab : D
log 15 = 4log 3 + 3log 15
=
1
❑
=
1
b
. 3log 3.5
3
log 3 + 3log 5
1
1
1+
b
a
( )
(1+ 1a ) =
=
=
b
13.
3
a+1
:b
a
=
a+1
ab
Jawab : C
1
√ 3 = 3log 33 + 3log 3 2
log 27 + 3log
1 3
. log 3 = 3 +
2
= 3. 3log 3 +
14.
1
2
=
3
1
2
Jawab : A
log 75 = log
300
4
= log 300 – log 4
= log 100.3 – log
2
2
= log 100 + log 3 – 2.log 2
= 2 + 0.4771 – 2.0,3010
= 2,4771 – 0,602 = 1,8751
15.
log
Jawab : A
10 x 3
y2
= log
10 x3 −¿
= log 10 + log
= 1 + 3.log
=
log
x 3−¿
x−¿
y2
y2
log
2.log
y
1+3 a−2b
3
16.
2
Jawab : E
log 25
3
×
log 8
5
×
2
log 9 = 2log
5
= 2.2log 5
×
×
3
log
3
3.3log 2
×
2
×
log
5
2
3
2.5log 3
= 2.3.2. 2log 5.5log 3.3log 2
= 12. 2log 2 = 12
17.
Jawab : E
2
log
( 2 x −6 )
=3
2
log
( 2 x −6 )
= 2log 23
= 23
2 x −6
=8
2 x −6
=8+6
2x
14
2 x =¿
18.
=7
Jawab : A
12
log 3 +
12
log 4 =
=
19.
5
14
2
=
x
12
12
log 3.4
log 12 = 1
Jawab : B
log 4
×
log 3
2
×
9
×
log 5 = 5log 22
= 2.5log 2
= 2.
1
2
.5log 2
×
×
2
log 3
2
2
log 3
32
×
log 3
1
2
×
×
log 5
3
log 5
log 5
3
= 1 . 5log 5 = 1
20.
Jawab : D
log 6 = log 2.3
= log 2 + log 3 = 0,3010 + 0,4771 = 0,7781
21.
2
Jawab : A
log 64 = 2log 26 = 6
22.
2
Jawab : E
log
1
128
= 2log 2-7 = -7
4
23.
Jawab : D
log 256 = log 162 = 2log 16 = 2
24.
×
1,20412 = 2,40824
Jawab : C
2
log 3 =
25.
log3
log 2
=
0,4771
= 1,58505
0,3010
Jawab : D
16
log 5 = x
24
log 3 = x
1
4
. 2log 5 =
log 5 =
2
2
x
4x
log 25 = 2log 52 = 2.2log 5 =
2.4 x
=
8x
5
PEMBAHASAN
1. Jawab : D
Ingat :
a
5
x=a n
log x=n ↔
log 25 = 2
↔
25=5
2
2. Jawab : A
Ingat :
2
a
log x=n ↔
x=a
log 32 = 2p
n
↔ 32 =
2
2p
3. Jawab : A
Ingat :
a
x=a n
log x=n ↔
7-2 =
1
49
log
7
↔
1
49
= -2
4. Jawab : E
2
4 ×10
5
log 4 + 2log 10 – 2log 5 = 2log
= 2log 8
= 2log 23
= 32log 2 = 3
× 1=3
5. Jawab : B
2
48
3
log 48 – 2log 3 = 2log
= 2log 16
= 2log
4
2
= 42log 2 = 4
× 1=4
6. Jawab : C
5
log 50 – 5log 2 = 5log
50
2
= 5log 25
= 5log
52
= 2 5log 5 = 2
× 1=2
7. Jawab : E
1
8
log ( 64 x × 4 )
=
8
log ( 64 x × 4 )
= 8log
64 x × 4
2
x
8
3− x
83− x
=
26 x ×22=
6x
3−x
83
8x
3
2 ×2 × 8 =8
26 x ×22 × 23 x =2 9
2
9 x +2
=2
9
=9
9 x+ 2
9 x=7
x=
7
9
8. Jawab : B
6
log 15 = 6log 3 . 3log 15
1
❑
=
. 3log 3 . 5
=
1
❑
. 3log 3 + 3log 5
=
1
❑
.
1+b
1
1+
a
=
(1+b)
=
1+b
a+1
a
=
(1+b ) a
a+1
9. Jawab : D
3
log 36 + 5log 100 – 3log 4 – 5log 4 = 3log 36 – 3log 4 + 5log 100 – 5log 4
= 3log
36
4
+ 5log
100
4
= 3log 9 + 5log 25
= 3log 32 + 5log 52
=2+2=4
10.
Jawab : A
b3
log
a
2
=
=
2
3
.blog a
2 1
2
. =
3 p 3p
2
11.
Jawab : E
2x = 18
2
log 18 = 2log 2.9 = 2log 2 + 2log 9
= 2log 2 + 2log 32
= 1 + 2 2log 3
12.
4
Jawab : D
log 15 = 4log 3 + 3log 15
=
1
❑
=
1
b
. 3log 3.5
3
log 3 + 3log 5
1
1
1+
b
a
( )
(1+ 1a ) =
=
=
b
13.
3
a+1
:b
a
=
a+1
ab
Jawab : C
1
√ 3 = 3log 33 + 3log 3 2
log 27 + 3log
1 3
. log 3 = 3 +
2
= 3. 3log 3 +
14.
1
2
=
3
1
2
Jawab : A
log 75 = log
300
4
= log 300 – log 4
= log 100.3 – log
2
2
= log 100 + log 3 – 2.log 2
= 2 + 0.4771 – 2.0,3010
= 2,4771 – 0,602 = 1,8751
15.
log
Jawab : A
10 x 3
y2
= log
10 x3 −¿
= log 10 + log
= 1 + 3.log
=
log
x 3−¿
x−¿
y2
y2
log
2.log
y
1+3 a−2b
3
16.
2
Jawab : E
log 25
3
×
log 8
5
×
2
log 9 = 2log
5
= 2.2log 5
×
×
3
log
3
3.3log 2
×
2
×
log
5
2
3
2.5log 3
= 2.3.2. 2log 5.5log 3.3log 2
= 12. 2log 2 = 12
17.
Jawab : E
2
log
( 2 x −6 )
=3
2
log
( 2 x −6 )
= 2log 23
= 23
2 x −6
=8
2 x −6
=8+6
2x
14
2 x =¿
18.
=7
Jawab : A
12
log 3 +
12
log 4 =
=
19.
5
14
2
=
x
12
12
log 3.4
log 12 = 1
Jawab : B
log 4
×
log 3
2
×
9
×
log 5 = 5log 22
= 2.5log 2
= 2.
1
2
.5log 2
×
×
2
log 3
2
2
log 3
32
×
log 3
1
2
×
×
log 5
3
log 5
log 5
3
= 1 . 5log 5 = 1
20.
Jawab : D
log 6 = log 2.3
= log 2 + log 3 = 0,3010 + 0,4771 = 0,7781
21.
2
Jawab : A
log 64 = 2log 26 = 6
22.
2
Jawab : E
log
1
128
= 2log 2-7 = -7
4
23.
Jawab : D
log 256 = log 162 = 2log 16 = 2
24.
×
1,20412 = 2,40824
Jawab : C
2
log 3 =
25.
log3
log 2
=
0,4771
= 1,58505
0,3010
Jawab : D
16
log 5 = x
24
log 3 = x
1
4
. 2log 5 =
log 5 =
2
2
x
4x
log 25 = 2log 52 = 2.2log 5 =
2.4 x
=
8x
5