Cambridge International Mathematics

Example 9 Self Tutor

Write these equations without logarithms:

a logD=2x+1 b logN¼ 1 : 301 ¡ 2 x

a logD=2x+1

) D=10^2 x+1

or D= (100)x£ 10

b logN¼ 1 : 301 ¡ 2 x

) N¼ 101 :^301 ¡^2 x

) N¼

101 :^301

102 x

¼

20

102 x

Example 10 Self Tutor

Write these equations without logarithms:

a logC= loga+ 3 logb b logG= 2 logd¡ 1

a logC= loga+ 3 logb

= loga+ logb^3

= log(ab^3 )

) C=ab^3

b logG= 2 logd¡ 1

= logd^2 ¡log 10^1

= log

μ

d^2

10

¶

) G=

d^2

10

EXERCISE 31D.2

1 Write the following as logarithmic equations in base 10 :

a y=ab^2 b y=

a^2

b

c y=d

p

p

d M=a^2 b^5 e P=

p

ab f Q=

p

m

n

g R=abc^2 h T=5

r

d

c

i M=

ab^3

p

c

2 Write these equations without logarithms:

a logQ=x+2 b logJ=2x¡ 1 c logM=2¡x

d logP¼ 0 :301 +x e logR¼x+1: 477 f logK=^12 x+1

3 Write these equations without logarithms:

a logM= loga+ logb b logN= logd¡loge

c logF= 2 logx d logT=^12 logp

e logD=¡logg f logS=¡2 logb

g logA= logB¡2 logC h 2 logp+ logq= logs

i ¡logd+ 3 logm= logn¡2 logp j logm¡^12 logn= 2 logP

k logN= 1 + logt l logP=2¡logx

Logarithms (Chapter 31) 633

IGCSE01

cyan magenta yellow black

(^05255075950525507595)
100 100
(^05255075950525507595)
100 100
Y:\HAESE\IGCSE01\IG01_31\633IGCSE01_31.CDR Monday, 27 October 2008 3:02:10 PM PETER