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MHR • Advanced Functions 12 Solutions 660

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Chapter 7 Review Question 9 Page 408<br />

a) log 6<br />

(8 ! 27) = log 6<br />

216<br />

= 3<br />

c) log 2 2 + log5 2 = log 4 + log 25<br />

= log(4 ! 25)<br />

= log100<br />

= 2<br />

! <strong>12</strong>8$<br />

b) log 4<br />

"<br />

# 8 %<br />

& = log 16 4<br />

= 2<br />

d) log3 2 + log<strong>12</strong>.5 = log9 + log<strong>12</strong>.5<br />

= log(9 !<strong>12</strong>.5)<br />

= log1<strong>12</strong>.5<br />

&= 2.05<br />

Chapter 7 Review Question 10 Page 408<br />

" 8 ! 4%<br />

a) log 7<br />

#<br />

$ 16 &<br />

' = log 2 7<br />

!<br />

b) log a 2 + log(3b) – log c = log 3a2 b$<br />

# & , a > 0, b > 0, c > 0<br />

" c %<br />

Chapter 7 Review Question 11 Page 408<br />

a) log a 2 + log b + log c = 2 log a + log b + log c, a > 0, b > 0, c > 0<br />

1<br />

b) log k ! log m = log k ! log m2<br />

= log k ! 1 log m, k > 0, m > 0<br />

2<br />

Chapter 7 Review Question <strong>12</strong> Page 408<br />

"<br />

a) log 2m + 6 %<br />

#<br />

$<br />

m 2 ! 9 &<br />

' = log " 2(m + 3) %<br />

#<br />

$ (m ! 3)(m + 3) &<br />

'<br />

" 2 %<br />

= log<br />

#<br />

$ m ! 3&<br />

' ,m > 3<br />

"<br />

b) log x2 + 2x !15%<br />

" (x + 5)(x ! 3) %<br />

$<br />

# x 2 ' = log<br />

! 7x +<strong>12</strong>&<br />

#<br />

$ (x ! 4)(x ! 3) &<br />

'<br />

"<br />

= log x + 5 %<br />

#<br />

$ x ! 4&<br />

' , x > 4 or x < !5<br />

<strong>MHR</strong> <strong>•</strong> <strong>Advanced</strong> <strong>Functions</strong> <strong>12</strong> <strong>Solutions</strong> 739

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