Basic Engineering Mathematics, Fifth Edition

Logarithms 117

y

0.5

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 15.1

Hence,logaa= 1. (Check with a calculator that

log 1010 =1andlogee=1.)

(c) loga 0 →−∞
Let loga 0 =xthenax=0 from the definition of a
logarithm.

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 15.2

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 →−∞