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The value of log((9)/(4))((1)/(2sqrt(3))...

The value of `log_((9)/(4))((1)/(2sqrt(3))sqrt(6-(1)/(2sqrt(3))sqrt(6-(1)/(2sqrt(3))sqrt(6-(1)/(2sqrt(3)))))...oo)` is

A

`-2`

B

`-1`

C

`-1//2`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
Let `x=(1)/(2sqrt(3))sqrt(6-(1)/(2sqrt(3))sqrt(6-(1)/(2sqrt(3))sqrt(6-(1)/(2sqrt(3)))))...oo`
`rArr x=(1)/(2sqrt(3))sqrt(6-1)`
`rArr 12x^(2)+x-6=0`
`rArr (3x-2)(4x+3)=0`
`rArr x=(2)/(3)`
`rArr log_((9)/(4))((1)/(2sqrt(3))sqrt(6-(1)/(2sqrt(3))sqrt(6-(1)/(2sqrt(3))sqrt(6-(1)/(2sqrt(3)))))...oo)`
`=log_((9)/(4))((2)/(3))=-(1)/(2)`
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