Cambridge International Mathematics

2 Copy and complete: Number Number as a power of 10 logof number

p

10

p (^310)
p
1000
p^1
10
3 Can you draw any conclusion from your table? For example, you may wish to comment on when
a logarithm is positive or negative.
Example 6 Self Tutor If the base for a
logarithm is not
given then we
assume it is 10.
a 2 b 20
ab
RULES FOR BASE 10 LOGARITHMS
These rules
correspond
closely to the
exponent laws.
log(xy) = logx+ logy
log
μ
x
y
¶
= logx¡logy
log(xn)=nlogx
Example 7 Self Tutor
Write as a single logarithm:
a log 2 + log 7 b log 6¡log 3 c 2 + log 9 d
log 49
log
¡ 1
7
¢
a log 2 + log 7
= log(2£7)
= log 14
b log 6¡log 3
= log
¡ 6
3
¢
= log 2
c 2 + log 9
= log 10^2 + log 9
= log(100£9)
= log 900
d
log 49
log
¡ 1
7
¢

=

log 7^2

log 7¡^1

=

2 log 7

¡1 log 7

=¡ 2

The rules for base 10 logarithms are clearly the same rules for general logarithms:

Logarithms (Chapter 31) 631

Use the property a=10loga to write the following numbers

as powers of 10 :

log 2¼ 0 : 301

) 2 ¼ 100 :^301

log 20¼ 1 : 301

) 20 ¼ 101 :^301

IGCSE01

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100 100
(^05255075950525507595)
100 100
Y:\HAESE\IGCSE01\IG01_31\631IGCSE01_31.CDR Thursday, 30 October 2008 12:05:29 PM PETER