26 Higher Engineering Mathematics
y
0.5
1.0
0 123
2 0.5
2 1.0
x
x 3
0.48
2
0.30
1
0
0.5
2 0.30
0.2
2 0.70
0.1
y 5 log 10 x 2 1.0
Figure 3.1
(ii) logaa= 1
Let logaa=xthenax=afrom the definition of
a logarithm.
Ifax=athenx=1.
Hence logaa=1. (Check with a calculator that
log 1010 =1andlogee=1)
y
2
1
0 123456 x
x 6 5 4 3 2 1 0.5 0.2 0.1
1.79 1.61 1.39 1.10 0.69 0 2 0.69 2 1.61 2 2.30
21
22
y 5 logex
Figure 3.2
(iii) loga 0 →−∞
Let loga 0 =xthenax=0 from the definition of
a logarithm.
Ifax=0, and a is a positive real number,
then x must approach minus infinity. (For
example, check with a calculator, 2−^2 = 0 .25,
2 −^20 = 9. 54 × 10 −^7 ,2−^200 = 6. 22 × 10 −^61 ,and
so on)
Hence loga 0 →−∞