If for x, y R, x > 0, y = log₁₀x + log₁₀x¹/3 + log₁₀x¹/9 +...... upto ∞ terms and (2 + 4 + 6 +.... + 2y)/(3 + 6 + 9 +..... + 3y) = 4/(log ₁₀x), then the ordered pair (x, y) is equal to:

Sequence and Series: JEE Main 2021 Mathematics question

JEE Main 2021 · 27 Aug, Morning shift · Q5326

JEE Main 202127 Aug, Morning shiftMathematicsMediumSequence and Series179× since 2002

If for x, y

\in

R, x > 0, y = log₁₀x + log₁₀x¹/3 + log₁₀x¹/9 + ...... upto

\infty

terms and

{{2 + 4 + 6 + .... + 2y} \over {3 + 6 + 9 + ..... + 3y}} = {4 \over {{{\log }_{10}}x}}

, then the ordered pair (x, y) is equal to :