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9. EBTANAS 1996
Jika x
1
dan x
2
adalah akar-akar persamaan : 2.9
2x-1
-5.3
2x
+18 = 0, maka x
1
+x
2
= .... A. 0
B. 2 C.
3
log 2 D. 2 -
3
log 2 E. 2 +
3
log 2
1
2.9
2x-1
-5.3
2x
+18 = 0 à basis 9
x
2.9
2x
.9
-1
-5.9
x
+18 = 0 x9 2.9
2x
-45.9
x
+18.9 = 0
2
9 2
9 .
18 9
2 1
= =
+ x x
Berarti : x
1
+x
2
= 2
1
. .
2
= +
+
c p
b p
a
x x
,maka a
c p
x x
=
+
2 1
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158
10. SPMB 2002No.20
Akar dari persamaan
3 1
5
27 3
+ -
=
x x
adalah.... A.
1 B.
2 C.
3 D.
4 E.
5
1
3 1
5
27 3
+ -
=
x x
à
9 3
1 5
3 3
+ -
=
x x
5x -1 = 3x +9 à 2x = 10
x = 5
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11. SPMB 2002No.16
Jika x 0 dan x ¹ 1 memenuhi
pq q
p
x x
x
1 1
1
. =
, p dan q bilangan rasional,maka hubungan antara p dan q
adalah.... A.
p +q = -1 B.
p +q = 1 C.
1 q
1 p
1 =
+
D. p.q = 1
E. p.q =-1
1
pq q
p
x x
x
1 1
1
. =
à
pq q
p
x x
1 1
1
=
+
pq pq
q p
1 =
+
à p +q = 1
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12. EBTANAS 2002No.21
Jika
1 1
3 2
6
+ -
=
x x
, maka x =.... A.
2
log 3 B.
3
log 2 C.
12
log 3 D.
3
log 6 E.
13
log 2
1
1 1
3 2
6
+ -
=
x x
à
1 x
1 x
3 2
2 .
3
+ -
=
Berarti :
2 log
x
3
= Kumpulan Rumus Cepat Matematika. Downloaded fr om
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161
1. UMPTN 1996
Jika
4
log4
x
.4 = 2 –x, maka x = …. A.
-1 B.
– ½ C.
½ D.
1 E.
2
1
4
log4
x
.4 = 2 –x
4
log 4
x+1
= 2 –x 4
x+1
= 4
2 –x
à x +1 = 2 –x x = ½
1
n m
n m
a a
a
+
= .
1
v a
a u
v u
= Û
= log
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162
2. UMPTN 1996
Jika x
1
dan x
2
adalah akar-akar persamaan logx
2
+7x +20 = 1, maka x
1
+x
2 2
-4x
1
.x
2
adalah…. A.
49 B.
29 C.
20 D.
19 E.
9
logx
2
+7x +20 = 1 =log 10 x
2
+7x +20 = 10 à x
2
+7x +10 = 0 x
1
+x
2 2
-4x
1
.x
2
= -7
2
-4.10 = 9
1
Akar-akar ax
2
+bx +c = 0 , x
1
dan x
2
Maka :
1
a b
x x
- =
+
2 1
1
a c
x x
=
2 1
.
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163
3. UMPTN 1996
Jika
2 log
1 log
27 1
3
= -
a
, maka nilai a yang memenuhi adalah….
A. 18
B. ¼
C. 2
D. 3
E. 4
1
2 log
1 log
27 1
3
= -
a
à
2 27
1 3
a log
1 =
-
1 –
3
log 3
-3
= a
2
1 – -3 = a
2
a
2
= 4 à a = 2
v a
a u
v u
= Û
= log
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164
4. UMPTN 1997
Jika 2 log x + log 6x –log 2x –log 27 = 0, maka x sama dengan....
A. 3
B. -3
C. 3 atau -3
D. 9
E. 9 atau -9
1
2 log x + log 6x –log 2x –log 27 = 0 1
log 27
. 2
6 .
log
2
=
x x
x
à
1 9
x
2
=
x
2
= 9 , berarti x = 3
1
a
log x +
a
log y =
a
log x.y
1
a
log x -
a
log y =
a
log
y x
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5. UMPTN 1997