Page 130 - Mathematics_Form_Two

Logarithms

Example 6�8 (b) log (0.01×100000)
10
Evaluate each of the following. = log 0.01+log 100000
10 10
(a) log (81 9)´
3 = log10 +log10 5
−2
(b) log (125 625)
5
= 2log10+5log10
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Solution
= (−2×1)+(5×1)
Mathematics for Secondary Schools 3 = log 3 + + log 3 3 2 Therefore, log (0.01 × 100,000) = 3.

=−2+5
+
´
=
(a) log (81 9) log 81 log 9
3
3
= 3

4
3
3

4log 3 2log 3
=
10
3
(4 × 1) + (2 × 1)
= ´ + ´
41 21
Example 6�10
42
=+
Write each of the following as a single
6
=
logarithm.
Therefore, log (81 9) 6 = .
3
(a) log 2 log 7+ a
a
(b) log (125 625) log 125 log 625 (b) log 4 log 5+ x
=
+
´
5
5
5
x
3
= log 5 + log 5 4 Solution
5
5
+
= 3log 5 4log 5
5
5
(3 × 1) + (4 × 1)
= ´ + ´ (a) log 2 log 7 log (2 7)+ a a = a ×
31 4 1
34
=+ log 14= a
= 7 (b) log 4 log 5 log (4 5)+ x x = a ×
Therefore, log (125 625) 7 = . log 20=
5 a
Example 6�9
Example 6�11
Find the value of each of the following:
10
(a) log (4 8) If log 2 0.3010,= log 3 0.4771,=
10
Evaluate each of
2
and log 5 0.6990.=
10
(b) log (0.01 × 100,000) the following:
10
Solution (a) log 6
10
=
´
(a) log (4 8) log 4 log 8 (b) log 30
+
2
2
2
2
= log 2 + log 2 3 10
2
2
= 2log 2 3log 2 (c) log 45
+
10
2
2
(2 × 1) + (3 × 1)
2 1 31
= ´ + ´ Solution
=+ (a) log 6 log 2 log 3= +
23
10
10
= 5 = 0.3010 04771+ 10
Therefore, log (4 8) 5 2 = . 0.7781=
124
Student's Book Form Two
11/10/2024 20:12:55
MATHEMATIC F2 v5.indd 124 11/10/2024 20:12:55
MATHEMATIC F2 v5.indd 124