Page 14 - MODULE & MORE ADDMATHS TG4

Matematik Tambahan Tingkatan 4 Bonus untuk Guru

BAB 4: INDEKS, SURD DAN LOGARITMA
Tahap Penguasaan Tafsiran
4 Mengaplikasikan pengetahuan dan kemahiran yang sesuai tentang indeks, surd dan logaritma dalam konteks
penyelesaian masalah rutin yang mudah.

1. Selesaikan setiap yang berikut.
Solve each of the following. 4
L (a) Ungkapkan setiap yang berikut sebagai satu logaritma tunggal.
Express each of the following as a single logarithm.
E (i) 4 log m – log n + 3 log p (ii) 3 log a – log b + 2 log c
1

a
a
a
= log m – log n + log p

x
4
x
2
x

3
1
M = log a a1 4 n 3 a 2 a = log a – log b + log c
2
m × p
2
3
x
x
x
2
3
a × c

B = log a1 n 2 = log x1 b 1 2
4 3
m p
2
3 2
a c
A = log x1 √b 2
R (b) Cari nilai bagi setiap yang berikut.
Find the value of each of the following.
A (i) 2 log 4 + log 5 – log 10 (ii) 3 log 2 + 2 log 3 – 2 log 6

4
2
4
4
2
2

2
= log 4 + log 5 – log 10
2
2
= log 2 + log 3 – log 6
3
N = log 2 21 10 2 2 2 = log 4 41 36 2 4 4
8 × 9
16 × 5
= log 8 = log 2

2 4
3
= log 2 1
2 2
= 3 = log 4
4
1
=
P 2
(c) Selesaikan setiap persamaan yang berikut.
B (i) log (2x + 3) = 2 + log (2x – 1) 1 1
Solve each of the following equations.

3
3
log (2x + 3) – log (2x – 1) = 2 (ii) 2 log 9 + log 81 = 2
p
4
p

D log 3 2x + 3 = 2 log 9 + log 81 = 2
3
3
1
1
4
2
p
p
2x – 1
2x + 3 = 3 log 3(3) = 2
p
2
8 2x – 1 p = 9 2
2
2x + 3 = 18x – 9
p = 3
2
16x = 12
3 p = 3
x =
4
(d) Diberi log 3 = 1.585 dan log 5 = 2.322, cari nilai bagi setiap yang berikut.
2
2
Given log 3 = 1.585 and log 5 = 2.322, find the value of each of the following.
2 2
(i) log 360 = log (5 × 8 × 9) (ii) log 33.75
2
2
2
= log (5 × 2 × 3 ) 135
3
2
2
= log 5 + 3 log 2 + 2 log 3 log 2 4 = log 135 – log 4
2
2
2
2
2
2
3
= 2.322 + 3 + 2(1.585) = log (5 × 3 ) – log 2
2
2
= 8.492 = log 5 + 3 log 3 – 2
2
2
= 2.322 + 3(1.585) – 2
= 5.077
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Bonus utk Guru.indd 8 12/11/2019 12:01 PM