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[ log 10 1 ]

(log 3 2 log 2 1 )

(log 3 2 log 2 1 )

2

3

10

10 10

10 10

 

 



.

2

3

Exercise 4.2

1. Find the value : (a) log 381 (b) log 535 (c) log 42 (d) log 25400

(e) log 5 35 ˜ 5

2. Find the value of x: (a) log 5 x 3 (b) logx 25 2 (c) 2
   16

1

logx 

3. Show that,
   (a) 5 log 105 log 1025 log 10125

(b) log 2 2 log 5 log 3 2 log 7

147

50

log 10 10  10  10  10

(c) 3 log 102  2 log 103 log 105 log 10360

4. Simplify :

(a)

80

81

3 log

24

25

2 log

9

10

7 log 10  10  10

(b) log 7 57 ˜ 7 log 333 log 42

(c) bc

a

cd

d

bc

c

ab

e e e e

2

3

3 3

3

33

3

33

log log log  3 log

4.5 Scientific or Standard form of numbers

We can express very large numbers or very small numbers in easy and small form by

exponents.

Such as, velocity of light = 300000 km/sec = 300000000 m/sec

= 3 u 100000000 m/sec. = 3 u 108 m/sec.

Again, radius of a hydrogen atom = 0 ˜ 00000000037 cm

=

10000000000

37

cm = 37 u 10 ^10 cm

= 3 ˜ 7 u 10 u 10 ^10 cm = 3 ˜ 7 u 10 ^9 cm

For convenience, very large number or very small number is expressed in the form

au 10 n, where 1 da 10 and nZ. The form au 10 n of any number is called the

scientific or standard form of the number.

Activity : Express the following numbers in scientific form :

(a) 15000 (b) 0 ˜ 000512