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…

If the sum of the first 20 terms of the series log71/2x+log71/3x+log71/4x+…is 460, then x is equal to:
  1. 72
  2. 71/2
  3. e2
  4. 746/21

Solution

Given log71/2x+log71/3x+log71/4x+…20 times =460
⇒  (2+3+4+…..+21)log7x=460
⇒  202(2+21)log7x=460
⇒  log7x=2
⇒  x=49

Asked in: JEE Main 2020 (05 Sep Shift 2)

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