Page 137 - Mathematics_Form_Two

Logarithms

Logarithms of numbers
Example 6�21
For many years, finding logarithms of
Given, numbers to base 10 has been tedious

0.845098
,
=
log 2= 0.30103 log 3 0.47712, 10 = , log 5 0.69897 log 7= due to the use of slide rules and tables
10
10
10
of common logarithms. For instance, to
log 2=log 2 0.30103 log 3 0.47712,0.30103 log= , 10 =3 0.47712= , log 5 0.69897 log 7=log 5 0.69897 log, 10 10 = , and , 10 =7 0.8450980.845098= use common logarithmic tables, it was
10
10
10
10
FOR ONLINE READING ONLY
Evaluate the following: necessary to express a number in standard
form, followed by identifying a mantissa
(a) log 7 (b) log 12 and a characteristic that are then used to
3
5
(c) log 15 (d) log 20 read logarithms of the respective numbers
6
7
from a table of common logarithms.
Solution Engage in Activity 6.1 to explore about Mathematics for Secondary Schools
log 7 0.845098
(a) log 7= 10 = = 1.77124 logarithms of numbers.
3 log 3 0.47712
10
log 7 0.845098 Activity 6�1: Determining the
log 7= 10 = = 1.77124
3
log 3 0.47712 logarithm of numbers
10
using calculators
log 12 log (2 ×3) 1. Explore the internet or other sources
2
10
10
(b) log 12 = log 5 = log 5 and learn different ways to determine
5
10
10
2
×
+
log 12 log ( 2 × ) 3 2log 2 log 3+ 2 0.30103 0.47712 the logarithms of numbers by using
calculators (mathematical software
log 12= 10 = 10 = 10 10 = = 1.55396
5
log 5 log 5 log 5 0.69897 and calculator devices).
10
10
10
2
+
log 12 log ( 2 × ) 3 2log 2 log 3 2 0.30103 0.47712× + 2. Determine logarithm values of
1,
x
log 12= 10 = 10 = 10 10 = = 1.55396 numbers in the ranges 0 <≤
5
log 5 log 5 log 5 0.69897 1 x<≤ 10, and numbers which are
10
10
10
greater than 10.
log 15 log (3 5× ) log 3 log 5+ 0.47712 0.69897+
(c) log 15= 10 = 10 = 10 3. Record your results in a table,
10
= 1.39166
=
7
log 7 log 7 log 7 compare the results from these
0.845098
10
10
10
log 15 log (3 5× ) log 3 log 5+ 0.47712 0.69897+ categories and share your
observations with others.
log 15= 10 = 10 = 10 10 = = 1.39166
7
log 7 log 7 log 7 0.845098
10
10
10
×
log 15 log (3 5 ) log 3 log 5 0.47712 0.69897+ Example 6�22
+
10
log 15= log 7 = log 7 = 10 log 7 10 = 0.845098 = 1.39166 Find the logarithm of each of the
10
7
10
10
10
2
log 20 log ( 2 ×5) following numbers, correct to 4 decimal
places:
10
(d) log 20 = log 6 = log 6 (a) 1 (d) 356 (g) 75,648
10
6
10
10
(b) 0.0253 (e) 2,534 (h) 64.667
2
log 20 log ( 2 × ) 5 2log 2 log 5 2 0.30103 0.69897
+
+
×
(c) −3
10
10
10
log 20= log 6 = 10 10 = log 2 log 3 = 0.30103 0.47712 = 1.67995 (f) 62.94
6
log 6
+
+
10
10
10
Solution
2
+
+
×
log 20 log ( 2 × ) 5 2log 2 log 5 2 0.30103 0.69897 To find the logarithm of a number,
log 20= log 6 = 10 10 = log 2 log 3 = 0.30103 0.47712 = 1.67995 enter the keystrokes of the logarithm
10
10
10
6
log 6
+
+
10
10
10
131
Student's Book Form Two
11/10/2024 20:13:03
MATHEMATIC F2 v5.indd 131
MATHEMATIC F2 v5.indd 131 11/10/2024 20:13:03