MHR • Advanced Functions 12 Solutions 660

d) 2log w + 3log w + 1 2 log !
1
$
w2 = 2log w + 3log w2
# & + 1
" % 2 (2)log w
= 2log w + 3 log w + log w
2
= 4 2 log+ 3 2 log w + 2 2 log w
= 9 log w, w > 0
2
Chapter 7 Section 3 Question 10 Page 385
"
a) log x2 ! 4%
" (x ! 2)(x + 2) %
$
# x ! 2
' = log
& #
$ x ! 2 &
'
= log( x + 2), x > 2
!
b) log x2 + 7x +12$
! (x + 4)(x + 3) $
#
" x + 3
& = log
% "
# x + 3 %
&
= log( x + 4), x > '3
"
c) log x2 ! x ! 6%
" (x ! 3)(x + 2) % "
$
# 2x ! 6
' = log
& #
$ 2(x ! 3) &
' d) log x2 + 7x +12%
" (x + 4)(x + 3) %
$
x 2 ' = log
# ! 9 & #
$ (x ! 3)(x + 3) &
'
"
= log x + 2 %
#
$ 2 &
' , x > 3 "
= log x + 4 %
#
$ x ! 3&
' , x > 3
Chapter 7 Section 3 Question 11 Page 385
!
a) V o
= log V $
2
# &
" %
V 1
!
b) i) V o
= log 10V $
1
# &
" %
= log10
= 1
V 1
!
ii) V o
= log 100V $
1
# &
" %
= log100
= 2
V 1
!
iii) V o
= log V $
1
# &
" %
= log1
= 0
V 1
Chapter 7 Section 3 Question 12 Page 385
a) log(10nx) = log10 + log n + log x
= 1+ log n + log x
translate y = log x up (1 + log n) units, n > 0
MHR • Advanced Functions 12 Solutions 696