Cambridge International Mathematics

Review set 31B

#endboxedheading

1aOn the same set of axes, sketch the graphs of y=3x and y= log 3 x.

b State the domain and range of each function.

2 Find the value of:

a log 2

p

2 b log 2 p^18 c logp 327 d log 927

3 Write the following in terms of logarithms:

a y=4x b y=a¡n

4 Write the following as exponential equations:

a y= log 2 d b M=^12 logak

5 Makexthe subject of:

a y= log 3 x b T= logb(3x) c 3 t=5£ 2 x+1

6 Find the inverse function f¡^1 (x) of:

a f(x)=6x b f(x)=^12 log 5 x

7 Solve forx, giving your answers correct to 4 significant figures:

a 3 x= 3000 b (1:13)x=2 c 2 (2

x)

=10

8

a What was the value of the banknote in 1970?

b What was the value of the banknote in 2005?

c

9 Write as a single logarithm:

a log 2 5 + log 23 b log 38 ¡log 32 c 2 log 5¡ 1 d 2 log 25 ¡ 1

10 Write as a logarithmic equation in base 10 :

a D=

100

n^2

b G^2 =c^3 d

11 Write as an equation without logarithms:

a logM=2x+1 b logG=^12 logd¡ 1

12 If log 3 7=a and log 3 4=b, find in terms ofaandb:

a log 3

¡ 4

7

¢

b log 328 c log 3

¡ 7

3

¢

13 Findyin terms ofcanddif:

a log 2 y= 2 log 2 c b log 3 y=^13 log 3 c¡2 log 3 d

14 Find log 7200 correct to 3 decimal places.

15 Use a graphics calculator to solve, correct to 4 significant figures:

a 3 x=0: 6 x+2 b log(2x)=(x¡1)(x¡4)

Logarithms (Chapter 31) 637

The value of a rare banknote has been modelled by V= 400£ 20 :^15 tUS dollars, wheretis the

time in years since 1970.

When is the banknote expected to have a value of$100 000?

IGCSE01

cyan magenta yellow black

(^05255075950525507595)
100 100
(^05255075950525507595)
100 100
Y:\HAESE\IGCSE01\IG01_31\637IGCSE01_31.CDR Friday, 31 October 2008 9:48:35 AM PETER