If the sum of the first 20 terms of the series log 7 1 / 2 x + log 7 1 / 3 x + log 7 1 / 4 x + … is 460 , then x is equal to:

Question

If the sum of the first 20 terms of the series log 7 1 / 2 x + log 7 1 / 3 x + log 7 1 / 4 x + … is 460 , then x is equal to:, 7 2, 7 1 / 2, e 2, 7 46 / 21

MARKS App · Accepted Answer

Given log 7 1 / 2 x + log 7 1 / 3 x + log 7 1 / 4 x + … 20 times = 460 ⇒ ( 2 + 3 + 4 + … . . + 21 ) log 7 x = 460 ⇒ 20 2 ( 2 + 21 ) log 7 x = 460 ⇒ log 7 x = 2 ⇒ x = 49

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