module 4 - indices and logarithms
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MODULE 4
INDICES AND LOGARITHMS
MODULPROGRAM IBNU SINAADDITIONAL MATHEMATICS
Terbitan :-YAYASAN PELAJARAN JOHORJABATAN PELAJARAN NEGERI JOHOR
INDICES AND LOGARITHMS FORM4
MODULE 4IBNU SINA
TOPIC : INDICES AND LOGARITHMS
Express Note :
Index - positive, negative zero and fractions
1. Value of numbers in the form of integer and fractional indices
5. Changing the base of logarithm
2. Law of indices am x an = a m+n
am an = a m - n
(a m ) n = a mn
6. Solving equation involving indices i. comparison of indices ii. comparison of bases iii.using logarithm
3. Logarithms - Definition - Finding logarithm of a number
7. Solving Logarithmic Equations i. using definition of logarithm ii. changing both sides of the equation
to single logarithm with the same base.
4. Laws of logarithm log a xy = log a x + log a y
log a = log a x - log a y
log a x m = m log a x
EXERCISE
1. Simplify the following.
a. 7 x-1 7 x-3 b. 2 4n 2 4 –n
c. 33m 9 m-1 ÷ 9 m+3 d. 25 2p+1 ÷ 125 1-2p
e. f.
g. 18 n+1 ÷ 10 1+n 15 1-2n h. 25 3n+3 ÷ 5 7n-3 125 n-1
2. Simplify the following indices in its simplest form
a. 2 n+1 + 2 n + 2 n-1 b. 4 x+1 - 4 x + 4 x-1
c. d. 5x + 6 5 x-1 +15 5 x-2
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INDICES AND LOGARITHMS FORM4
3. Solve the following equations
a. b. 9 p+2 = 27
c. 2(4 q+4) = 32 3q-3 d. 81 3+x = 3 9 6x+1
e. 5 x+1 + 5x = 150 f.
4. Express each of the following as a single logarithm.
a. b.
c. d.
5. Given that log a 2 = x and log a 5 = y, express each of following in terms of x and/or y
a. b.
c. d.
e. f.
6. Given that log a p = r and log a q = s, express each of following in terms of r and/or s.
a. b. log a pq3
c. d.
7. Solve the following equations of indices and logarithms.
a. 3 x = 5 b. 2 x-2 = 15
c. 7 3x-2 = 77 d. 2 x 5 x-2 = 15
e. 5 x+2 5 2x-1 = 100 f. 2 x+1 - 5 x+2 = 0
g. h.
i. j.
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INDICES AND LOGARITHMS FORM4
8. Solve the following equations
a. log 3 (2x – 1) + log 2 4 = 5 b. log 4 (x – 2) + 3log 2 8 = 10
c. log 2 (x + 5) = log 2 (x – 2) + 3 d. log 5 (4x – 7) = log 5 (x – 2) + 1
SPM QUESTIONS
1. Given log3x = m and log 2x = n. Find logx 24 in terms of m and n.
2. Given log3 x = p and log 9 y = q. Find log 3 xy2 in terms of p and q.
3. Given and , express in terms of m and p.
4. Given , Express T in terms of V.
5. Solve the equation
6. Solve the equation .
7. Solve the equation .
8.Given that and , express in terms of p and r.
9.Solve the equation .
10. Given that , express y in terms of x.
11. Solve the equation .
12. Solve the equation .
13. Solve the equation
14.Simplify without using calculator
15. Given 3 log xy2 = 4 + 2log y – log x, where x and y are integers. Prove xy =10
16. Solve the equation 3log2
x = 81
END OF MODULE 4
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INDICES AND LOGARITHMS FORM4
MODULE 4 - ANSWERS TOPIC : INDICES AND LOGARITHMS
PAPER 11a b c d
e f g h
2a b c d
3a x = -1 b c d
e x = 2 f x = 14a b c d
5a 3x b c x + y +3 d y - 2
e 3y – 3x - 3 f
6a b r + 3s c -2r – 5s d
7a 1.465 b 5.907 c 1.411 d 2.574 e – 0.139 f -2.756 g h p = 3 i x = 2 j x = 2258a x = 14 b x = 5 c x = 3 d x = 3
SPM Questions1 2 p + 4q 3 2p – m - 1 4
5 x = 1.677 6 x = - 3 7 8 3r – 2p + 1
9 x = 1 10 y = 2x 11 12 x = 1
13 x = 2,3 14 15 16 x=16
END OF MODULE 4
PROGRAM IBNU SINA TAHUN 2010(ALL A’s) Page 5