Cambridge International Mathematics

To solve logarithmic equations, we can sometimes write each side as a power of 10.

Example 13 Self Tutor

Solve forx: log 3 x=¡ 1

log 3 x=¡ 1

)

logx

log 3

=¡ 1 flogab=

logb

loga

g

) logx=¡1 log 3

) logx= log(3¡^1 )

) logx= log

¡ 1

3

¢

) x=^13

EXERCISE 31E

1 Solve forxusing logarithms, giving answers to 4 significant figures:

a 10 x=80 b 10 x= 8000 c 10 x=0: 025

d 10 x= 456: 3 e 10 x=0: 8764 f 10 x=0:000 179 2

2 Solve forxusing logarithms, giving answers to 4 significant figures:

a 2 x=3 b 2 x=10 c 2 x= 400

d 2 x=0: 0075 e 5 x= 1000 f 6 x=0: 836

g (1:1)x=1: 86 h (1:25)x=3 i (0:87)x=0: 001

j (0:7)x=0: 21 k (1:085)x=2 l (0:997)x=0: 5

3 The weight of bacteria in a culturethours after it has been established

is given by W=2: 5 £ 20 :^04 tgrams.

After what time will the weight reach:

a 4 grams b 15 grams?

4 The population of bees in a hivethours after it has

been discovered is given byP= 5000£ 20 :^09 t.

After what time will the population reach:

a 15 000 b 50 000?

5 Answer theOpening Problemon page 625.

6 Show that log 5 13 =

log 13

log 5

. Hence find log 513.

7 Find, correct to 3 significant figures:

a log 212 b log 3100 c log 751 d log 2 (0:063)

8 Solve forx:

a log 2 x=2 b log 5 x=¡ 2 c log 2 (x+2)=2 d log 5 (2x)=¡ 1

Logarithms (Chapter 31) 635

IGCSE01

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Y:\HAESE\IGCSE01\IG01_31\635IGCSE01_31.CDR Friday, 31 October 2008 9:46:39 AM PETER