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If log2 (log8x)=log8(log2x), find the va...

` If log_2 (log_8x)=log_8(log_2x),` find the value of `(log_2x)^2.`

A

1

B

2

C

3

D

Not defined

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Verified by Experts

The correct Answer is:
B
If `log_(2)(log_(8)x) = log_(8)` …………..
Let `p = log_(2)x`
`:. Log_(2)((p)/(3)) = (log_(2)p)/(3) implies (p^(3))/(27) = p implies p^(2) = 27`
so `N = 27 implies sqrt(3N) = sqrt(81) =9`
`log_(3)sqrt(3N) = log_(3)9 = 2`
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