Add Maths F4 Topical Test 5 (BL)

50/2SULIT

NAMA: _______________________________________________ TINGKATAN: ______________

TOPICAL TEST 5: Indices and Logarithms

UJIAN TOPIKAL 5: Indeks dan Logaritma

1Given that p = 2x and q = 3x, express in terms of p and q.

Diberi bahawa p = 2x dan q = 3x, ungkapkan dalam sebutan p dan q.

[2 marks / 2 markah]

2Show that 25n + 52(n + 1) + 25n + 1 is divisible by 51 by all positive integer values of n.

Tunjukkan bahawa 25n + 52(n + 1) + 25n + 1 boleh dibahagikan tepat dengan 51 bagi semua nilai integer positif n.


3Find the value of 12n + 1 .

Cari nilai bagi 12n + 1 .


4Simplify 25n and show that the answer is always positive.

Permudahkan 25n dan tunjukkan bahawa jawapannya sentiasa positif.


5Given that 2 log10 x + 2 = log10 y, express x in terms of y.

Diberi bahawa 2 log10 x + 2 = log10 y, ungkapkan x dalam sebutan y.


6Given that p = loga 2 and q = loga 3, express loga 72 in terms of p and q.

Diberi bahawa p = loga 2 dan q = loga 3, ungkapkan loga 72 dalam sebutan p dan q.


7Given that log2 5 = a and log2 7 = b, express log2 4.9 in terms of a and b.

Diberi bahawa log2 5 = a dan log2 7 = b, ungkapkan log2 4.9 dalam sebutan a dan b.


8Given that loga= x and loga m2n3 = y, express loga in terms of x and y.

Diberi bahawa loga= x dan loga m2n3 = y, ungkapkan loga dalam sebutan x dan y.


9Given that logb 2 = h and logb 3 = k, express logb in terms of h and k.

Diberi bahawa logb 2 = h dan logb 3 = k, ungkapkan logb dalam sebutan h dan k.[4 marks / 4 markah]

10Find the value of log2 16 + 2 log2 3 + log2 8 + 2 log2 10 + log2 9 log2 135 log2 5 without using a calculator.

Cari nilai bagi log2 16 + 2 log2 3 + log2 8 + 2 log2 10 + log2 9 log2 135 log2 5 tanpa menggunakan kalkulator.


11Find the value of log5 25 log3 7 log7 3.

Cari nilai bagi log5 25 log3 7 log7 3.[3 marks / 3 markah]

12Given that = 400p, show that 20p = and find the value of p.

Diberi bahawa = 400p, tunjukkan bahawa 20p = dan cari nilai p.


13Given that log3 x = u, express logx 9x2 in terms of u.

Diberi bahawa log3 x = u, ungkapkan logx 9x2 dalam sebutan u.


14Given that log3 a = m and log3 b = n, express log9 in terms of m and n.

Diberi bahawa log3 a = m dan log3 b = n, ungkapkan log9 dalam sebutan m dan n.[4 marks / 4 markah]

15Given that log3 = p, express log in terms of p.

Diberi bahawa log3 = p, ungkapkan log dalam sebutan p.


16Given that log3 P log9 Q = 2, express P in terms of Q.

Diberi bahawa log3 P log9 Q = 2, ungkapkan P dalam sebutan Q.


17Solve the equation 273x 1 = 95x

Selesaikan persamaan 273x 1 = 95x


18Solve the equation 3433x = 492x + 5.

Selesaikan persamaan 3433x = 492x + 5.


19Solve the equation 62x 3 = 9x.

Selesaikan persamaan 62x 3 = 9x.


20Given that 25(52n + 1) = 125n, find the value of n.

Diberi bahawa 25(52n+1) = 125n, cari nilai n.


21Solve the equation 274x + 2 = .

Selesaikan persamaan 274x + 2 = .


22Solve the equation 5x + 2 + 5x + 3 = 30.

Selesaikan persamaan 5x + 2 + 5x + 3 = 30.


23Given that log9 x = log3 6, find the value of x.

Diberi bahawa log9 x = log3 6, cari nilai x.


24Given that log4 ab = 4 log4 a + 2 log4 b, express a in terms of b.

Diberi bahawa log4 ab = 4 log4 a + 2 log4 b, ungkapkan a dalam sebutan b.


25Solve the equation 1 + log2 (2x + 3) = log2 6x.

Selesaikan persamaan 1 + log2 (2x + 3) = log2 6x.


1Given that log3 2 = 0.631 and log3 5 = 1.465, calculate each of the following without using a calculator.

Diberi bahawa log3 2 = 0.631 dan log3 5 = 1.465, hitungkan setiap yang berikut tanpa menggunakan kalkulator.

(a)log3 1.5

(b)log5 50


2Solve each of the following equations:

Selesaikan setiap persamaan yang berikut:

(a)log10 a = 100log2

(b)9y . 302y 2 = 90y . 32y 1


3Given that y = axb, where a and b are constants, find the values of a and b if x = 4, y = 6 and x = 25, y = 15.

Diberi bahawa y = axb, dengan keadaan a dan b ialah pemalar, cari nilai a dan b jika x = 4, y = 6 dan x = 25, y = 15.


4Diagram 1 shows a right-angled triangle and a square.

Rajah 1 menunjukkan sebuah segitiga bersudut tegak dan sebuah segiempat sama.

Diagram 1 Rajah 1

The area of the right-angled triangle is same as the square. Find the positive values of x.

Luas segitiga bersudut tegak itu adalah sama dengan luas segiempat sama. Cari nilai-nilai positif x.


5(a)Solve the equation / Selesaikan persamaan:

2 log a + 1 = log (9a 2)

(b)Given that a = 3p, find the values of p.

Diberi bahawa a = 3p, cari nilai-nilai p.


6Given that 2 log2 = 2 + 2 log2 x, express y in terms of x. If 2y2 6y = 20x2, find the values of x and y, where x > 0.

Diberi bahawa 2 log2= 2 + 2 log2 x, ungkapkan y dalam sebutan x. Jika 2y2 6y = 20x2, cari nilai x dan nilai y, di mana keadaan x > 0.


7(a)The value of a precious stone at the beginning of year 1970

was RM12 000. This value increased continuously so that

after a period of t years, the value of the stone was given

by expression 12 000 (1.03)t.

Nilai seketul batu permata pada permulaan tahun 1970 ialah RM12 000. Nilainya bertambah secara berterusan supaya selepas t tahun, nilai bagi batu permata diberi oleh ungkapan 12000 (1.03)t.

(i)Calculate the value of the stone, to the nearest RM, at the beginning of 1985.

Hitungkan nilai batu permata itu, kepada RM yang terhampir, pada permulaan tahun 1985.

(ii)Find the year in which the value of the stone first reached RM21 000.

Cari tahun di mana nilai bagi batu permata itu kali pertama mencapai RM21 000.

(b)Solve the equation logx 9 + log3 x = 3.

Selesaikan persamaan logx 9 + log3 x = 3.


8(a)Given that 2p = 3q = , express r in terms of p and q.

Diberi bahawa 2p = 3q = , ungkapkan r dalam sebutan p dan q.

(b)Simplify log2 n . logn 64 . log8 2n. Then, find the value of n if the simplified terms is equal 10.

Permudahkan log2 n . logn 64 . log8 2n. Seterusnya, cari nilai n jika sebutan yang dipermudahkan sama dengan 10.


9Solve each of the following equations:


(a)log 2y = 1 + log (20 3y)

(b)10 . 2x 8 = 2 . 4x(c)t log2 2t + log2 4t 2 + t = 8


10Solve each of the following:

Selesaikan setiap persamaan berikut:

(a)16x 1 = 1

(b)2 log3 p = log3 48 1

(c)log2 2x = 2 + log2 (x 4)


11(a)Simplify 4(3n) + 3n 2 3n + 1 in the simplest form and find

the value of n if the simplified expression is equal to .

Permudahkan 4(3n) + 3n 2 3n + 1 dalam bentuk termudah dan cari nilai n jika ungkapan yang dipermudahkan adalah sama dengan .

(b)Solve the equation / Selesaikan persamaan:

log2 [log2 (2x + 3)] = log3 9


12(a)Given that log2 p = y, express logp 8 in term of y.

Diberi bahawa log2 p = y, ungkapkan logp 8 dalam sebutan y.

(b)Given that logp 3k logp 3 = 0, find the value of k.

Diberi bahawa logp 3k logp 3 = 0, cari nilai k.

(c)Given that log7 2 = 0.356 and log7 5 = 0.827, find the value of log3 70.

Diberi bahawa log7 2 = 0.356 dan log7 5 = 0.827, cari nilai bagi log3 70.


13(a)Given that 2x . 9x = 21 x . 3x 1, find the value of 12x.

Diberi bahawa 2x . 9x = 21 x . 3x 1, cari nilai bagi 12x.

(b)By means of substitution a = 2x, find the value of x such that 4x 1 = (2x). Give the answer correct to two decimal places.

Dengan penggantian a = 2x, cari nilai x dengan keadaan 4x 1 = (2x). Beri jawapan betul kepada dua tempat perpuluhan.


14(a)Given that h = 3p and k = 2q, express log4 k log3 in

terms of p and q.

Diberi bahawa h = 3p dan k = 2q, ungkapkan log4 k log3 dalam p dan q.

(b)Solve each of the following equations:


(i)log2 (x 3) = 2

(ii)log2 (2y2 11) = log2 84 2


15(a)Given that 2x . 16y = 128 and = , find the values

of x and y.

Diberi bahawa 2x . 16y = 128 dan =, cari nilai x dan y.

(b)Solve the equation log (2x + 6) = 1 + log (2x 1).

Selesaikan persamaan 1og (2x + 6) = 1 + log (2x 1).


PAPER 2 KERTAS 2

6

SULIT Navision (M) Sdn. Bhd. (690640-P)

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Add Maths F4 Topical Test 5 (BL)