1.

Let `a=(log)_3(log)_3 2.`An integer `k`satisfying `1

Answer» Correct Answer - A
We have,
`a = "log"_(3)("log"_(3) 2) rArr 3^(a) = "log"_(3) 2 rArr "log"_(2) 3 = 3^(-a)`
Now, `1 lt 2^((-k+3^(-a))) lt 2`
`rArr 0 lt -k + 3^(-a) lt 1`
`rArr 0 lt -k + "log"_(2) 3 lt 1`
`rArr k lt "log"_(2) 3 lt k +1`
Now, `"log"_(2) 3 gt 1 rArr k +1 gt 1 rArr k gt0`
and, `"log"_(2) 3 lt 2 rArr k lt 2`
`therefore 0 lt k lt 2 rArr k = 1 " " [therefore "k is an integer"]`


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