In the interval 0 , 2 π , sum of all the roots of the equation sin π log 3 1 x = 0 is

Question

In the interval 0 , 2 π , sum of all the roots of the equation sin π log 3 1 x = 0 is, 3 2, 4, 9 2, 13 3

MARKS App · Accepted Answer

π log 3 1 x = k π , k ∈ I log 3 1 x = k ⇒ x = 3 - k Possible values of k are – 1 , 0 , 1 , 2 , 3 , . . . . . . . S = 3 + 1 + 1 3 + 1 3 2 + 1 3 3 + ..... ∞ = 4 + 1 / 3 1 - 1 / 3 = 4 + 1 2 = 9 2

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