The value of x satisfying the equation `root(3)(5)^(log_(5)5^(log_(5)5^(log_(5)5^(log_(5)((x)/(2))`= 3, is
The value of x satisfying the equation
`root(3)(5)^(log_(5)5^(log_(5)5^(log_(5)5^(log_(5)((x)/(2))`= 3, is
A. 1
B. 3
C. 18
D. 54
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Correct Answer - 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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