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Compute the following (81^(1/((log)5 9))...

Compute the following `(81^(1/((log)_5 9))+3^(3/((log)_(sqrt(6))3)))/(409)dot((sqrt(7))^(2/((log)_(25)7))-(125)^((log)_(25)6))`

A

0

B

1

C

2

D

3

Text Solution

Verified by Experts

The correct Answer is:
B
`(81^((1)/(log_(5)9))+3^((3)/(log_(sqrt(6)3))))/(409)((sqrt(7))^((2)/(log_(25)7))-(125)^(log_(25)6))`
`=(9^(log_(9)5^(2))+3^(log_(3)(sqrt(6))^(3)))/(409)(7^(log_(7)25)-5^(log_(5)6^(3//2)))`
`= (25+6sqrt(6))/(409)[25-6sqrt(6)]`
`=(625-216)/(409)=(409)/(409)=1`
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