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The value of 0. 2^(logsqrt(5)1/4+1/8+1/(...

The value of `0. 2^(logsqrt(5)1/4+1/8+1/(16)+)` is `4` b. `log4` c. `log2` d. none of these

A

4

B

log 4

C

log 2

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
We have,
`1/4+1/8+1/16+…=(1//4)/(1-1//2)=1/2`
Hence,
`0.2^(log_(sqrt5(1/4+1/8+1/16+..)))=0.2^(log_(sqrt5)""1/2)`
`=(1/5)^(log_(sqrt5)""1/2)`
`=(5^(-1))^(2log_(5)""1/2)`
`(5)^(-2log_(5)""1/2)`
`=(5)^(log_(5)4)=4`
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