132 Logarithms (Chapter 5)
Example 2 Self Tutor
Use your calculator to write the following in the form 10 x wherexis correct to
4 decimal places:
a 8 b 800 c 0 : 08
a 8
=10lg 8
¼ 100 :^9031
b 800
=10lg 800
¼ 102 :^9031
c 0 : 08
=10lg 0:^08
¼ 10 ¡^1 :^0969
3aUse your calculator to find lg 41, giving your answer correct to 4 decimal places.
b Hence, write 41 as a power of 10.
4 Use your calculator to write the following in the form 10 xwherexis correct to 4 decimal places:
a 6 b 60 c 6000 d 0 : 6 e 0 : 006
f 15 g 1500 h 1 : 5 i 0 : 15 j 0 :000 15
5 Explain why you cannot find the logarithm of a negative number.
Example 3 Self Tutor
a Use your calculator to find: i lg 2 ii lg 20
b Explain why lg 20 = lg 2 + 1.
ailg 2¼ 0 : 3010
ii lg 20¼ 1 : 3010
b lg 20 = lg(2£10)
¼lg(10^0 :^3010 £ 101 )
¼lg 10^1 :^3010 fadding exponentsg
¼ 1 : 3010
¼lg 2 + 1
6aUse your calculator to find: i lg 3 ii lg 300
b Explain why lg 300 = lg 3 + 2.
7aUse your calculator to find: i lg 5 ii lg 0: 05
b Explain why lg 0:05 = lg 5¡ 2.
Example 4 Self Tutor
Findxif:
a lgx=3 b lgx¼¡ 0 : 271
a lgx=3
) 10 lgx=10^3
) x= 1000
b lgx¼¡ 0 : 271
) 10 lgx¼ 10 ¡^0 :^271
) x¼ 0 : 536
Remember that
10 =lgx x.
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100 100 4037 Cambridge
Additional Mathematics
Y:\HAESE\CAM4037\CamAdd_05\132CamAdd_05.cdr Tuesday, 21 January 2014 2:47:23 PM BRIAN