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Section 3.3 Properties of Logarithms 217
42. log 43. lnz ln z 12 1 6 z3 3 log 2 ln z
6 z 44. ln t 3 ln t 13 1 3 ln t
45. ln xyz ln x ln y ln z 46. ln xy
z
ln x ln y ln z
47.
log 3 a 2 bc 3 log 3 a 2 log 3 b log 3 c 3 48.
2 log 3 a log 3 b 3 log 3 c
log 5 x 3 y 3 z log 5 x 3 log 5 y 3 log 5 z
3 log 5 x 3 log 5 y log 5 z
49.
lna 2 a 1 ln a 2 lna 1 12
50.
lnzz 1 2 ln z lnz 1 2
2 ln a 1 2 lna 1, a > 1
ln z 2 lnz 1
51.
53.
ln x 3 y 1 3 ln x 52.
y
1 ln x ln y
3
1 3 ln x 1 3 ln y
ln
x 2 1
x 3 lnx2 1 ln x 3 54.
lnx 1x 1 3 ln x
lnx 1 lnx 1 3 ln x, x > 1
ln
x 2
ln
y 3 ln x2
y 312 1 2 ln x2
y 3
x
1 2 ln x2 ln y 3
1 2 ln x 3 ln y
2
ln x 3 2 ln y
x 2 1 ln x lnx2 1
ln x lnx 2 1 12
ln x 1 2 lnx2 1
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55.
57.
ln
x 4 y
z 5 ln x 4 y ln z 5 56.
y 1 lnx 3 x 4
(a)
−2
14
−2
ln x 4 lny ln z 5
4 ln x 1 ln y 5 ln z
2
y 2 3 ln x lnx 4
(c) The graphs and table suggest that
y 1 y 2 for x > 0. In fact,
22
y 1 lnx 3 x 4 ln x 3 lnx 4
3 ln x lnx 4 y 2 .
(b)
log b
x y4
z 4 log b
x y 4 log b z 4
log b x 12 log b y 4 log b z 4
1 2 log b x 4 log b y 4 log b z
x 0.5 1 1.5 2 3 10
y 1 0.5754 1.6094 2.9211 3.8712 5.2417 9.5468
y 2 0.5754 1.6094 2.9211 3.8712 5.2417 9.5468