BAB 5 INDEKS DAN LOGARITMA

MODUL 5 / TG 4 INDEKS DAN LOGARITMA

BAB 5
INDEKS

DAN
LOGARITMA

MODUL SOLAF MATEMATIK TAMBAHAN M5-1

MODUL 5 / TG 4 INDEKS DAN LOGARITMA

KERTAS 1

1. Selesaikan

Solve

8x = 1 [2 m /Aras R]
32

2. Selesaikan persamaan [2m/ Aras R]
Solve the equation

16 x-1 = 8 x+3

3. Selesaikan persamaan

Solve the equation

42x = 1 [2 m / Aras R]
8

4. Selesaikan [2 m / Aras R]
Solve

27 4x = 812x+5

MODUL SOLAF MATEMATIK TAMBAHAN M5-2

MODUL 5 / TG 4 INDEKS DAN LOGARITMA

5. Selesaikan persamaan
Solve the equation
323x = 47 x+4

6. Selesaikan persamaan [2 m /Aras R]
Solve the equation [4 m /Aras S]
[2 m /Aras R]
32x-1 = 5x [3 m / Aras R]

7. Selesaikan persamaan
Solve the equation

165x = 49x-6

8. Selesaikan persamaan

Solve the equation

273x+3 = 1
9x-3

MODUL SOLAF MATEMATIK TAMBAHAN M5-3

MODUL 5 / TG 4 INDEKS DAN LOGARITMA

9. Selesaikan persamaan
Solve the equation
22x+1 -13(2x ) - 24 = 0

[ 4 m /Aras S]

10. Diberi log3 K - log9 L = 2 , ungkapkan K dalam sebutan L
Given that log3 K - log9 L = 2 , express K in terms of L.

[4 m /Aras S]

11. Diberi log p 3 = r dan log p 7 = s, ungkapkan log p æ 49 p ö dalam sebutan r dan s.
èç 27 ÷ø

Given that log p 3 = r and log p 7 = s , express log p æ 49 p ö in terms of r and s.
çè 27 ÷ø

[4 m /Aras S]

MODUL SOLAF MATEMATIK TAMBAHAN M5-4

MODUL 5 / TG 4 INDEKS DAN LOGARITMA

12. Diberi log5 2 = q dan log5 9 = p, ungkapkan log5 8.1dalam sebutan q dan p
Given that log5 2 = q and log5 9 = p , express log5 8.1 in terms of q and p.
[4 m /Aras S]

13. Selesaikan persamaan
Solve the equation

3 + log3(2x -1) = log3 x.

[3 m /Aras S]

14. Diberi logx 2 = p dan logx 7 = q, ungkapkan log x æ 56 ö÷ødalam sebutan p dan q.
èç x2

Given that logx 2 = p and logx 7 = q , express log x æ 56 ö in terms of p and q.
èç x2 ø÷

[4 m /Aras

S]

15. Diberi log3 mn = 3 + 2 log3 m - log3 n, ungkapkan m dalam sebutan n.

Given that log3 mn = 3 + 2 log3 m - log3 n express m in terms of n.
[4 m /Aras S]

MODUL SOLAF MATEMATIK TAMBAHAN M5-5

MODUL 5 / TG 4 INDEKS DAN LOGARITMA

16. Diberi log9 y = log3 18, cari nilai y.
Given that log9 y = log3 18, find the value of y.

[3 m /Aras S]

17. Diberi log3 m = v dan log3 n = w, ungkapkan log9 æ 81m ÷øö dalam sebutan v dan w.
èç n

Given that log3 m = v and log3 n = w , express log9 æ 81m ö in terms of v and w.
èç n ø÷

[4 m /Aras S]

18. Selesaikan persamaan
Solve the equation

log3 x - log3 (4x + 1) = -2.

19. Sesaikan persamaan [3 m /Aras
S]
Solve the equation
[3 m / Aras S]
5 x-1 - 5x = - 4
25

MODUL SOLAF MATEMATIK TAMBAHAN M5-6

MODUL 5 / TG 4 INDEKS DAN LOGARITMA [3 m / Aras R]
[3m / Aras T]
20. Selesaikan
Solve
814x = 272x+5

21. Selesaikan persamaan
Solve the equation
3(53x+1) = 36

22. Nilaikan [3 m / Aras R ]
Evaluate

2 -3 3

8 3 ´16 4 ÷ 4 2

MODUL SOLAF MATEMATIK TAMBAHAN M5-7

MODUL 5 / TG 4 INDEKS DAN LOGARITMA [3 m / Aras R]
[3 m / Aras R]
23. Selesaikan persamaan [3 m / Aras S ]
Solve the equation [3 m / Aras R ]

2x+4 - 2x+3 = 1

24. Permudahkan
Simplify

3n+2 ´ 9n+3
27 n+3

25. Selesaikan persamaan
Solve the equation
3x2 - 96-2x = 0

( )26. Selesaikan 27t = 9 3t-1 , cari nilai t .
( )Solve 27t = 9 3t-1 , find the value of t.

MODUL SOLAF MATEMATIK TAMBAHAN M5-8

MODUL 5 / TG 4 INDEKS DAN LOGARITMA

27. Jika logm 3 = p dan logm 5 = q, nyatakan dalam sebutan p dan/ atau q
If logm 3 = pand logm 5 = q, state in terms of p and/or q
(a) logm 125Error! Reference source not found.
(b) log15 135
[4 m / Aras S]

28. Diberi p = 3r dan q = 3s, ungkapkan dalam sebutan r dan s

Given p = 3r and q = 3s, state in term of r and s

(a) log 3 ( pq )
27

(b) log27 p + log81q

[ 4 m / Aras S]

MODUL SOLAF MATEMATIK TAMBAHAN M5-9

MODUL 5 / TG 4 INDEKS DAN LOGARITMA

KERTAS 2

1. Diberi log2 15 = 3.9069dan log2 (53) = 0.7370, tanpa menggunakan kalkulator
saintifik atau jadual empat angka, carikan nilai,

Given log2 15 = 3.9069 and log 2 ( 5 ) = 0.7370, without using scientific calculator or
3
four digit table, find the value

(a) log2 3,

(b) Seterusnya, cari nilai bagi log 2 37.5
Hence, find the value of log 2 37.5

Error! Reference
source not found.

2. (a) Diberi log8 n = 1 , cari nilai n
3

Given that log8 n = 1 , find the value of n. .[ 1m/Aras R]
3 [ 4 m /Aras S]

(c) Diberi 2r = 3s = 6t , ungkapkan tdalam sebutan r dan s

Given that 2r = 3s = 6t , express t in terms of r and s.

(d) Diberi y = kxm dengan keadaan k dan m ialah pemalar , y = 4apabila x = 2

dan y = 8apabila x = 5, cari nilai k dan m.

Given that y = kxm where k and m are constants . y = 4when x = 2and

y = 8when x = 5, find the values of k and m. [5 m /Aras T]

Error! Reference source not found. Error! Reference source not found.

3. (a) Selesaikan persamaan [ 3 m / Aras S]
(e) Solve the equation

log3 x = log9 (x + 6)

Diberi log7 x3 y = 5 - 2(log7 x + 2 log7 y) Error! Reference source not found.,
dengan keadaan x dan y ialah integer positif. Ungkapkan y dalam sebutan x.

Given log7 x3 y = 5 - 2(log7 x + 2 log7 y)such that x and y are positive interger
Express y in term of x.

[4 m /Aras S]

MODUL SOLAF MATEMATIK TAMBAHAN M5-10

MODUL 5 / TG 4 INDEKS DAN LOGARITMA

4. Selesaikan persamaan
Solve the equations

(a) 22x+3 = 30 + 2x

(b) log2 5 x + log4 16x = 6

[7 m / Aras T]

5. Nilai sebuah rumah meningkat sebanyak 5% pada setiap awal tahun daripada harga
asal. Jika nilai rumah itu bermula dengan RM90 000, selepas t tahun, didapati nilainya

RM p, diberi oleh p = 90000(1.05)t .

The value of a house increases by 5% at the beginning of each year. If the initial
value of the house is RM90 000, the value of the house after t years, RM p, is given by

p = 90000(1.05)t .

Cari
Find

(a) nilai rumah itu selepas 6.5 tahun,
the value of the house after 6.5 years

(b) bilangan tahun minimum untuk nilai rumah itu melebihi RM150 000.

minimum number of years for the value of the house to be more than
RM150 000

[5 m / Aras
T]

6. Selesaikan persamaan serentak
Solve the simultaneous equations

log9 y = 1+ log3 x

9x = 3y

7. Selesaikan persamaan [7 m /Aras T]
Solve the equation [5 m /Aras T]

log 2 (x + 5) + log 4 (5 - x)2 = 2 + log8 çæ 9 ÷ö3
è 4 ø

8. (a) Diberi y = 3x , ungkapkan 32x-1 - 3x+1dalam sebutan y .

Given y = 3x , express 32x-1 - 3x+1in terms of y .
[3 m / Aras

S]
(a) Seterusnya, selesaikan persamaan 32x-1 - 3x+1 + 6 = 0.

Hence or other wise, solve the equation 32x-1 - 3x+1 + 6 = 0 [5 m / Aras T]

MODUL SOLAF MATEMATIK TAMBAHAN M5-11

MODUL 5 / TG 4 INDEKS DAN LOGARITMA

9. (a) Ungkapkan log3 (2x + 1) - 5log9 x2 + 4 log3 x sebagai logaritma tunggal.

Express log3 (2x + 1) - 5log9 x2 + 4 log3 x as a single logarithm.
[ 4 m / Aras S]

(b) Seterusnya selesaikan persamaan

Hence, solve the following equation

log3 (2x + 1) - 5log9 x2 + 4 log3 x = 3

[ 2 m / Aras S]

10. (a) Diberi log2 xy = 2 + 3log2 x - log2 y. Ungkapkan y dalam sebutan x.
Given that log2 xy = 2 + 3log2 x - log2 y. Express y in terms of x.
[ 4 m / Aras S]

(c) Selesaikan persamaan 2 + log3 (x -1) = log3 x.

Solve the equation 2 + log3 (x -1) = log3 x.

[ 3 m / Aras S]

MODUL SOLAF MATEMATIK TAMBAHAN M5-12