Cambridge International Mathematics

EXERCISE 31C

1 Write as a single logarithm:

a log 3 2 + log 38 b log 29 ¡log 23 c 3 log 5 2 + 2 log 53

d log 3 8 + log 37 ¡log 34 e 1 + log 34 f 2 + log 35

g 1 + log 73 h 1 + 2 log 43 ¡3 log 45 i 2 log 3 m+ 7 log 3 n

j 5 log 2 k¡3 log 2 n

2 If log 2 7=p and log 2 3=q, write in terms ofpandq:

a log 221 b log 2

¡ 3

7

¢

c log 249 d log 227

e log 2

¡ 7

9

¢

f log 2 (63) g log 2

¡ 56

9

¢

h log 2 (5:25)

3 Writeyin terms ofuandvif:

a log 2 y= 3 log 2 u b log 3 y= 3 log 3 u¡log 3 v

c log 5 y= 2 log 5 u+ 3 log 5 v d log 2 y=u+v

e log 2 y=u¡log 2 v f log 5 y=¡log 5 u

g log 7 y= 1 + 2 log 7 v h log 2 y=^12 log 2 v¡2 log 2 u

i log 6 y=2¡^13 log 6 u j log 3 y=^12 log 3 u+ log 3 v+1

4 Without using a calculator, simplify:

a

log 216

log 24

b

logp 16

logp 4

c

log 525

log 5

¡ 1

5

¢ d

logm 25

logm

¡ 1

5

¢

Logarithms in base 10 are calledcommon logarithms.

y= log 10 x is often written as just y= logx, and weassumethe logarithm has base 10.

Your calculator has a log key which is for base 10 logarithms.

Discovery Logarithms

#endboxedheading

The logarithm of any positive number can be evaluated using the log key on your calculator. You will

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

10

100

1000

100 000 105 log(100000) = 5

0 : 1

0 : 001

D LOGARITHMS IN BASE 10 [3.10]

need to do this to evaluate the logarithms in this discovery.

630 Logarithms (Chapter 31)

What to do:

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Y:\HAESE\IGCSE01\IG01_31\630IGCSE01_31.CDR Friday, 31 October 2008 9:46:05 AM PETER