Page 134 - Mathematics_Form_Two

log x = 1 log 4 + 1 log 27
a
a
a
3
2
Logarithms 1 1
= log 4 + log 27 3
2
a
a
Solution 1 1
( )
( ) +
Given log x = log 2 log- 2 3. It implies = log 2 2 2 log 3 3 3
a
a
2
2
that, = log 2 log 3+ a
a
log x = log æ 2 ö = log a (2 3 )
ç ÷
2
2
è 3 ø = log 6
a
FOR ONLINE READING ONLY
2 2 . log x = log 6 log 6.
x =
Mathematics for Secondary Schools Therefore, x = 2 . Therefore, x = 6.
Thus, x =
a
a
Thus, log x =
3
3
a
a
6
x =

3
Example 6�19
Example 6�17
log6
Given that log 2 0.30103= and Simplify log 216 .
log3 0.47712= . Calculate the value of Solution
log 48. log6 = log6
log 216 log6 3
Solution log6
4
log48 log= (2 ´ ) 3 (factors of 48) = 3log6
= log 2 + log3 (logarithm of a product) = 1
4
3
= 4log 2 log3 (logarithm of a power)+ log6 1
Therefore, = .
= 4(0.30103) + 0.47712 log 216 3
= 1.68124
Therefore, log 48 1.68124.= Exercise 6�3
1. Find the value of each of the
following expressions.
Example 6�18
(a) log 3 (9 81 )
Find the value of x given that
(b) log 5 (5 25 625  )
1 1
log x = 2 log 4 + 3 log 27 . (c) log (100 0.0001 )
a
a
a
Solution (d) log 7 (49 343 )
1 1
log x = log 4 + log 27 2. Calculate the value of each of the
a
2 a 3 a following expressions.
1 1
3
= log 4 + log 27 3 (a) log 49
2
7
a
a
1 1
( )
= log 2 2 2 log 3 3 3 128
( ) +
a
a
= log 2 log 3+ a Student's Book Form Two
a
= log (2 3 )
11/10/2024 20:13:00
MATHEMATIC F2 v5.indd 128 a 11/10/2024 20:13:00
MATHEMATIC F2 v5.indd 128
= log 6
a
log x = log 6
a
a
 x = 6