This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
1. (a)
bxayba
abyaby
x
x
x
logloglogloglog)log(log
+=
+=
=
=
(b) When x = 1, log y = 0.8. 0.8 = log a + log b ……(1) When x = 3, log y = 0.5. 0.5 = log a + 3 log b ……(2)
(2) − (1):
d.p.) 1 to(cor. 7.010
15.0 log log 23.0
15.0
=
=
−=
=−
−bb
b
By substituting log b = −0.15 into (1), we have
d.p.) 1 to(cor. 9.810
95.0 log15.0 log8.0
95.0
=
=
=
−=
aa
a
(c) From (b), xy 0.150.95 log −=
When y = 100,
71.050.15
0.150.9520.150.95100 log
−=
−=
−=
−=
xx
xx
2. (a) 36 = 62 236log6 =
(b) 23
3 3327 ==
2327log3 =
3. (a)
33log
27log7189log7log189log
33
3
333
=
=
=
⎟⎠
⎞⎜⎝
⎛=−
(b)
52log2log 5
2log2log
2log32log
2log)84(log
2log8log4log
6
6
6
56
6
6
6
6
6
66
=
=
=
=
×=
+
(c)
41221
7log7log
49log7log
7log
27
21
7
7
749
=
=
=
=
4. (a)
5124820
48244
863
4
163
4log
1)63(log)4(log)63(log1)4(log
8
88
88
=
=
−=
=−
=⎟⎠
⎞⎜⎝
⎛−
=−−
−=−
x
xxx
xx
xxxx
xx
(b)
42)2(
8)(
8
8
5.18log
2
32
3
32
32
23
23
5.1
=
=
=
=
=
=
=
x
x
x
xx
5. (a) (i) From the graph, when x = 3, y = −1.6. 6.13log0.5 −=
(ii) 5.3log5.3log 0.52 −= From the graph, when x = 3.5, y = −1.8.
8.15.3log 5.0 −= 8.1)8.1(5.3log2 =−−= (b) (i) From the graph, when y = 0.5, x = 0.7. The solution of 5.0log0.5 =x is x = 0.7.
(ii)
3.1log3.1log3.1log
0.5
0.5
2
=
−=−
−=
xxx
From the graph, when y = 1.3, x = 0.4. The solution of 3.1log2 −=x is x = 0.4. 6. (a)