Question

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)`

Answer 1

Correct Answer - 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`