Cambridge Additional Mathematics

(singke) #1
134 Logarithms (Chapter 5)

EXERCISE 5B


1 Write an equivalent exponential equation for:
a log 10 100 = 2 b log 10 10 000 = 4 c log 10 (0:1) =¡ 1
d log 10

p
10 =^12 e log 2 8=3 f log 3 9=2

g log 2 (^14 )=¡ 2 h log 3

p
27 = 1: 5 i log 5

³
p^1
5

́
=¡^12

2 Write an equivalent logarithmic equation for:
a 22 =4 b 43 =64 c 52 =25
d 72 =49 e 26 =64 f 2 ¡^3 =^18
g 10 ¡^2 =0: 01 h 2 ¡^1 =^12 i 3 ¡^3 = 271

Example 6 Self Tutor


Find:
a log 216 b log 50 : 2 c log 105

p
100 d log 2

³
p^1
2

́

a log 216
= log 224
=4

b log 50 : 2
= log 5 (^15 )
= log 55 ¡^1
=¡ 1

c log 105

p
100

= log 10

¡
102

¢^15

= log 1010

2
5
=^25

d log 2

³
p^1
2

́

= log 22
¡^12

=¡^12

3 Find:
a log 10 100 000 b log 10 (0:01) c log 3

p
3 d log 28
e log 264 f log 2128 g log 525 h log 5125
i log 2 (0:125) j log 93 k log 416 l log 366
m log 3243 n log 23

p
2 o logaan p log 82

q logt

³
1
t

́
r log 66

p
6 s log 41 t log 99

4 Use your calculator to find:
a log 10152 b log 1025 c log 1074 d log 100 : 8
5 Solve forx:
a log 2 x=3 b log 4 x=^12 c logx81 = 4 d log 2 (x¡6) = 3

6 Simplify:
a log 416 b log 24 c log 3

¡ 1
3

¢
d log 104

p
1000

e log 7

³
p^1
7

́
f log 5 (25

p
5) g log 3

³
p^1
27

́
h log 4

³
1
2
p
2

́

i logxx^2 j logx

p
x k logmm^3 l logx(x

p
x)

m logn

³
1
n

́
n loga

³
1
a^2

́
o loga

μ
1
p
a


p logm

p
m^5

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Additional Mathematics
Y:\HAESE\CAM4037\CamAdd_05\134CamAdd_05.cdr Tuesday, 21 January 2014 2:47:31 PM BRIAN

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