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The value of `x` satisfying the equation `3sqrt(5)^(log)_5 5^(((log)_5(log)_5log_5(x/2)))` 1 (b) 3 (c) 18 (d) 54

A

1

B

3

C

18

D

54

Text Solution

Verified by Experts

The correct Answer is:
D
Using ` a^(log_(a)N) = N` repeatedly, we get
`(root(3)5)^(log _(5)(x/2)) = 3`
`rArr 5^(log_(5)(x/2)^(1//3)) = 3`
`rArr (x/2)^(1//3)= 3`
` rArr x/2 = 27`
`rArr x = 54`
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