Cambridge International Mathematics

Review set 31A

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1aOn the same set of axes, sketch the graphs of y=2x and y= log 2 x.

b What transformation would map y=2x onto y= log 2 x?

c State the domain and range of y= log 2 x.

2 Copy and complete:

a logaax= b if y=bx then x= , and vice versa.

3 Find the value of:

a log 216 b log 3

¡ 1

3

¢

c log 2

p

32 d log 48

4 Write the following in terms of logarithms:

a y=5x b y=7¡x

5 Write the following as exponential equations:

a y= log 3 x b T=^13 log 4 n

6 Makexthe subject of:

a y= log 5 x b w= log(3x) c q=

72 x

3

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

a f(x)=4£ 5 x b f(x) = 2 log 3 x

8 Solve forx, giving your answers correct to 5 significant figures:

a 4 x= 100 b 4 x=0: 001 c (0:96)x=0:013 74

9 The population of a colony of waspstdays after discovery is given by P= 400£ 20 :^03 t:

a How big will the population be after 10 days?

b How long will it take for the population to reach 1200 wasps?

10 Write as a single logarithm:

a log 12¡log 2 b 2 log 3 + log 4 c 2 log 2 3 + 3 log 25

11 Write as a logarithmic equation in base 10 :

a y=

a^3

b^2

b M=3

q

a

b

12 Write as an equation without logarithms:

a logT=¡x+3 b logN= 2 logc¡logd

13 If log 2 3=a and log 2 5=b, find in terms ofaandb:

a log 215 b log 2

¡

(^123)
¢
c log 210
14 Findyin terms ofuandvif:
a log 2 y= 4 log 2 u b log 5 y=¡2 log 5 v c log 3 y=^12 log 3 u+ log 3 v
15 Find log 315 correct to 4 decimal places.
16 Use a graphics calculator to solve, correct to 4 significant figures:
a 2 x=4¡ 3 x b logx=3¡x
636 Logarithms (Chapter 31)
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Y:\HAESE\IGCSE01\IG01_31\636IGCSE01_31.CDR Monday, 27 October 2008 3:02:19 PM PETER