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The value 4^(5log(4sqrt(2))(3-sqrt(6))-6...

The value `4^(5log_(4sqrt(2))(3-sqrt(6))-6log_8(sqrt(3)-sqrt(2)))` is

A

3

B

6

C

9

D

27

Text Solution

Verified by Experts

The correct Answer is:
C
`4^(5log_(4sqrt(2))(3-sqrt(6))-6 log_(8)(sqrt(3)-sqrt(2)))`
`= 4^(2 log_(2)(sqrt(3)(sqrt(3)-sqrt(2)))-2 log_(2)(sqrt(3)-sqrt(2)))`
`= 4^(2 log_(2)sqrt(3))`
`= 2^(log_(2)(sqrt(3))^(4))`
= 9
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