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If log((sqrt(bsqrt(bsqrt(bsqrt(b)))))(sq...

If `log_((sqrt(bsqrt(bsqrt(bsqrt(b)))))(sqrt(asqrt(asqrt(asqrt(asqrt(a))))))=x log_(b) a`, then x =

A

`(32)/(16)`

B

`(31)/(15)`

C

`(31)/(30)`

D

`(1)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
C
(i) Use, `sqrt(asqrt(asqrt(a...n " terms"))) = a^((2^(n-1//2^(n)))` and then `log_(b^(n))a^(m) = (m)/(n) log_(b)a` and simplify LHS.
(ii) Compare LHS and RHS and find the value of x.
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