Question

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Answer 1

Solution :-

i)

Given that

(6.023×35×10²³)/2.814

Let X = (6.023×35×10²³)/2.814

On taking Logarithms both sides then

log X = log [(6.023×35×10²³)/2.814]

We know that

log ab = log a + log b

log X = [(log 6.023+ log 35 + log 10²³)] / 2.814

log a^m = m log a

log X = [(log 6.023+ log 35 +23 log 10)] / 2.814

log a/b = log a- log b

log X = log 6.023+ log 35 +23 log 10- log 2.814

Now,

By Logarithmic table

log 6.023 = 0.7771

log 35 = 1.5441

(+)

_______________

2.3212

log 2.814 = 0.4493

(-)

_______________

1.8719

________________

Log X = 1.8719 ×10²³

Now anti log of 1.8719 = 74.46

Therefore, we have 74.46×10²³

(6.023×35×10²³)/2.814 = 74.46×10²³

ii)

Given that

(4.286-3.323)/(16.32×6.923)

= 0.963/(16.32×6.923)

Let X = 0.963/(16.32×6.923)

On taking Logarithms both sides then

log X = log [ 0.963/(16.32×6.923)]

log ab = log a + log b

log X = log 0.963/(log 16.32+log 6.963)

log a/b = log a- log b

=> log X =log 0.963 - (log 16.32+log 6.963)

log 16.32 = 1.2127

log 6.963 = 0.8403

(+)

________________

2.0530

________________

log 0.963 = -1 . 9863

= 2.0530

(-)

_________________

-3.9333

_________________

log X = -3.9333

Anti log of -3.9333 = 0.8576

(4.286-3.323)/(16.32×6.923) = 0.8576

Answer :-

i) (6.023×35×10²³)/2.814 = 74.46×10²³

ii) (4.286-3.323)/(16.32×6.923) = 08576

Used formulae:-

♦ log ab = log a + log b

♦log a/b = log a- log b

♦ log ab = log a + log b

Answer 2

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Given that

(6.023-35-10/2.014

Let X=(6.023-35-107/2514

On taking Logerithms coth sides then

og X-loc 10.023-35-10 V/2.814)

We know that

|log ab = log a + log b

og x=log 6.023+ op 35log 10

log a'm-m log a

og x=(og 6.023+ og 35+23 og 101/

2.814

log a/b = log a-log b

log-loc 6,023+log 35 +23 log 10+ log

2.814

Now,

By Logarithmic table

og 6.033=0.7771

og 35 15441

2.3212

og 2.814 0.4493

1.8719

Lap X=1879-10²

Now anti log of 18719 = 74.46

Therefore, we have 74-46-0

(6.023-35-10)/2.814-74.46-10"

H)

Given that

(4.286-3.323(16.32-6,923)

Ontlung Logerithms both sides then

og X-log[ 0.963/6.32-6.923|||

log ab-log a-log b

og X-log 0.903/op 10.326963)

log a/blog a log b

→log X-log 0.963 -log16.32 og

6.9831

og 16.32- 12127

og 6.963-08403

2.0530

og 0.863-19663

-2,0530

3.9333

og X-1.9333

Anti log of 3.933308576

(4.286-3,323p(16.32-6.923) -0.8576

Answer :

0) (6.023-35-10)/2.814-74-16-10

(4.286-3.323) (16.32-6.923)-08576

Used formulae:

log ab-loga + log b

iog a/blog-log b

log ab= log a-log b