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The value of log10(sqrt(3-sqrt(5))+sqrt(...

The value of `log_10(sqrt(3-sqrt(5))+sqrt(3+sqrt(5)))` is

A

`1//2`

B

`1//4`

C

`3//2`

D

`3//4`

Text Solution

Verified by Experts

The correct Answer is:
A
`log_(10)((sqrt(6-2sqrt(5))+sqrt(6+2sqrt(5)))/(sqrt(2)))`
`log_(10)(((sqrt(5)-1)+(sqrt(5)+1))/(sqrt(2)))`
`=log_(10)((2sqrt(5))/(sqrt(2)))`
`log_(10)sqrt(10)=(1)/(2)`
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