MHR • Advanced Functions 12 Solutions 660

Chapter 7 Section 3 Question 5 Page 384
! 54$
a) log 3
"
# 2 %
& = log 27 3
= 3
! 320$
c) log 4
"
# 5 %
& = log 64 4
= 3
!
b) log
"
#
50 000
5
$
%
& = log10 000
= 4
! 2 $
d) log
"
# 200%
& = log0.01
= '2
Chapter 7 Section 3 Question 6 Page 384
a) log 16
2 3 + log 16
8 2 ! log 16
2 = log 16
8 + log 16
64 ! log 16
2
# 8 " 64&
= log 16
$
% 2 '
(
= log 16
256
= 2
1
b) log 20 + log 2 + log125 3
= log 20 + log 2 + log5
= log(20 ! 2 ! 5)
= log 200
&= 2.301
Chapter 7 Section 3 Question 7 Page 385
a) log 7 c + log 7 d b) log 3 m – log 3 n
1
c) logu + log v 3 = logu + 3log v d) log a + log b 2
! log c 2 = log a + 1 log b ! 2log c
2
e) log 2
(5! 2) = log 2
5+ log 2
2
= log 2
5+1
f) log 5
(25! 2) = log 5
25+ log 5
2
= 2 + log 5
2
Chapter 7 Section 3 Question 8 Page 385
Answers may vary. A sample solution is shown.
log 5
(5!10) = log 5
5+ log 5
10
= 1+ log 5
10
Since log 5 10 can be simplified again using 10 = 5 × 2, the original solution is the simplest result.
MHR • Advanced Functions 12 Solutions 694