Cambridge International Mathematics

EXERCISE 31D.1

1

a 8 b 80 c 800 d 0 : 8 e 0 : 008

f 0 : 3 g 0 : 03 h 0 :000 03 i 50 j 0 : 0005

2 Write as a single logarithm in the form logk:

a log 6 + log 5 b log 10¡log 2 c 2 log 2 + log 3

d log 5¡2 log 2 e^12 log 4¡log 2 f log 2 + log 3 + log 5

g log 20 + log(0:2) h ¡log 2¡log 3 i 3 log

¡ 1

8

¢

j 4 log 2 + 3 log 5 k 6 log 2¡3 log 5 l 1 + log 2

m 1 ¡log 2 n 2 ¡log 5 o 3 + log 2 + log 7

3 Explain why log 30 = log 3 + 1 and log(0:3) = log 3¡ 1

4 Without using a calculator, simplify:

a

log 8

log 2

b

log 9

log 3

c

log 4

log 8

d

log 5

log

¡ 1

5

¢

e

log(0:5)

log 2

f

log 8

log(0:25)

g

log 2b

log 8

h

log 4

log 2a

5 Without using a calculator, show that:

a log 8 = 3 log 2 b log 32 = 5 log 2 c log

¡ 1

7

¢

=¡log 7

d log

¡ 1

4

¢

=¡2 log 2 e log

p

5=^12 log 5 f log^3

p

2=^13 log 2

g log

³

p^1

3

́

=¡^12 log 3 h log 5 = 1¡log 2 i log 500 = 3¡log 2

6 74 = 2401¼ 2400

Show that log 7¼^34 log 2 +^14 log 3 +^12.

LOGARITHMIC EQUATIONS

The logarithm laws can be used to help rearrange equations. They are particularly useful when dealing with

exponential equations.

Example 8 Self Tutor

Write the following as logarithmic equations in base 10 :

a y=a^3 b^2 b y=

m

p

n

a y=a^3 b^2

) logy= log(a^3 b^2 )

) logy= loga^3 + logb^2

) logy= 3 loga+ 2 logb

b y=

m

p

n

) logy= log

μ

m

n

1

2

¶

) logy= logm¡logn

(^12)
) logy= logm¡^12 logn
632 Logarithms (Chapter 31)
Write as powers of 10 using a=10loga:
IGCSE01
cyan magenta yellow black
(^05255075950525507595)
100 100
(^05255075950525507595)
100 100
Y:\HAESE\IGCSE01\IG01_31\632IGCSE01_31.CDR Thursday, 30 October 2008 11:59:02 AM PETER