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The difference of roots of the equation ...

The difference of roots of the equation `((log)_(27)x^3)^2=(log)_(27)x^6` is .......

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The correct Answer is:
8
` (log_(27)x^(3))^(2) = log_(27)x^(6)`
` or (3 log_(27)x) ^(2) = 6 log_(27)x`
` or 3 log_(27)x(3 log _(27)x-2) = 0`
` rArr x = 1 or log_(27)x = 2/3`
` rArr x = (27)^(2//3) = 9`
Difference = 9 - 1 = 8
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