Cambridge Additional Mathematics

Logarithms (Chapter 5) 139

Example 11 Self Tutor

Write the following equations without logarithms:

a lgy=xlg 4 + lg 3 b log 2 M= 3 log 2 a¡ 5

a lgy=xlg 4 + lg 3

) lgy=lg4x+lg3

) lgy=lg(3£ 4 x)

) y=3£ 4 x

b log 2 M= 3 log 2 a¡ 5

) log 2 M= log 2 a^3 ¡log 225

) log 2 M= log 2

μ

a^3

32

¶

) M=

a^3

32

EXERCISE 5D.1

1 Write the following as logarithmic equations in base 10 , assuming all terms are positive:

a y=2x b y=x^3 c M=d^4

d T=5x e y=

p

x f y=7£ 3 x

g S=^9

t

h M= 100£ 7 x i T=5

p

d

j F=

1000

p

n

k S= 200£ 2 t l y=

r

15

x

2 Write the following equations without logarithms:

a lgy=xlg 7 b lgD=lgx+lg2 c logaF= loga 5 ¡logat

d lgy=xlg 2 + lg 6 e lgP=^12 lgx f lgN=¡^13 lgp

g lgP=3lgx+1 h lgy=x¡lg 2 i lgy=2lgx¡ 1

j log 2 T= 5 log 2 k+1 k log 3 P= 4 log 3 n¡ 2 l log 2 y=4x+3

3 Suppose lgy=3lgx¡lg 2.

a Writeyin terms ofx, without using logarithms.

b Findywhen: i x=2 ii x=4

4 Suppose lgy=^13 x+2.

a Writeyin the form y=a(10bx) wherea,b 2 Q.

b Findywhen: i x=0 ii x=3

5 Copy and complete:

a If there is apowerrelationship betweenyandx, for example y=5x^3 , then there is alinear

relationship between lgy and ......

b If there is anexponentialrelationship betweenyandx, for example y=4£ 2 x, then there is

alinearrelationship between ...... and ......

4037 Cambridge

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Y:\HAESE\CAM4037\CamAdd_05\139CamAdd_05.cdr Thursday, 23 January 2014 2:12:55 PM BRIAN