Cambridge Additional Mathematics

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

cyan magenta yellow black

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