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Question: Answered & Verified by Expert
If for x,yR, x>0, y=log10x+log10x1/3+log10x1/9+upto terms and 2+4+6++2y3+6+9++3y=4log10x, then the ordered pair x, y is equal to
MathematicsSequences and SeriesJEE MainJEE Main 2021 (27 Aug Shift 1)
Options:
  • A 106, 6
  • B 106, 9
  • C 102, 3
  • D 104, 6
Solution:
1453 Upvotes Verified Answer
The correct answer is: 106, 9

2+4+6++2y3+6+9++3y=4log10x

21+2+3+----y31+2+3+----y=4log10x

log10x=6

x=106

Now

y=log10x+log10x13+log10x19---

=1+13+19---log10x

=11-13log10x=9

So, x, y=106, 9

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