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What is the value of `(log_(27)9xxlog_(16)64)/(log_(4)sqrt(2))`?

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What is the value of
`(log_(27)9xxlog_(16)64)/(log_(4)sqrt(2))`?
A. `(1)/(6)`
B. `(1)/(4)`
C. 8
D. 4
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1 Answer

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Best answer
Correct Answer - D
The given logarithm expression
`(log_(27)9log_(16)64)/(log_(4)sqrt(2))`
is simplified as :
`(log9)/(log27)xx(log64)/(log16)xx(log4)/(logsqrt(2))`
`=(2log3)/(3log3)xx(6log2)/(4log2)xx(2log2)/((1)/(2)log2)`
`=(2)/(3)xx(6)/(4)xx4=4`
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