The sum of all roots of `sin(pi(log)_3(1/x))=0`in `(0,2pi)`is`3/2`(b) 4(c) `9/2`(d) `(13)/3`
A. `3//2`
B. 4
C. `9//2`
D. `13//3`
A. `3//2`
B. 4
C. `9//2`
D. `13//3`
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Correct Answer – C
`pi log_(3) (1/x)=k pi, k in I`
`log_(3) (1/x)=k or x=3^(-k)`
The possible values of k are `-1, 0, 1, 2, 3,…`
`S=3+1+1/3+1/3^(2)+1/3^(3)+…oo=3/(1-1/3)=9/2`