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What is the value of (log(27)9xxlog(1...

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

A

`(1)/(6)`

B

`(1)/(4)`

C

8

D

4

Text Solution

Verified by Experts

The correct Answer is:
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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