Cambridge Additional Mathematics

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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Additional Mathematics
Y:\HAESE\CAM4037\CamAdd_05\132CamAdd_05.cdr Tuesday, 21 January 2014 2:47:23 PM BRIAN