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98. The value of x satisfying the equati...

98. The value of x satisfying the equation `((sqrtpi)^(log_pi(x))).((sqrtpi)^(log_(pi^2)(x))).((sqrtpi).^(log_(pi^4)(x))).((sqrtpi)^(log_(pi^8)(x)))...oo=3` is equal to

A

`sqrt(pi)`

B

`pi`

C

3

D

`(1)/(3)`

Text Solution

Verified by Experts

The correct Answer is:
C
We have
`(sqrt(pi))^(log_(pi)x).(sqrt(pi))^(log_(pi)4x).(sqrt(pi))^(log_(pi)8x)`
`rArr (sqrt(pi))^((1+(1)/(2)+(1)/(4)+(1)/(8)+…oo)log_(pi)x)=3`
`rArr (sqrt(pi))^(2log_(pi)x)=3`
`rArr pi^(log_(pi)x=3`
`rArr x = 3`
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