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If (21. 4)^a=(0. 00214)^b=100 , then the...

If `(21. 4)^a=(0. 00214)^b=100` , then the value of `1/a-1/b` is

A

0

B

1

C

2

D

4

Text Solution

Verified by Experts

The correct Answer is:
C
`(21.4)^(a) = 100`
` rArr a log(21.4) = 2`
` :. Log(21.4) = 2//a` …(i)
From ` (0.00214)^(b) = 100`, we get
` b(log 0.00214)= 2`
` or b log(214.4 xx 10^(-4)) = 2`
` or b = 2/(log 21.4-4) = 2/(2/a-4) = 1/(1/a - 2) = a/(1-2a)`
` rArr 1/b = (1-2a)/a`
` rArr 1/a - 1/b = 2`
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