If for , upto terms and , then the ordered pair is equal…

MATHEMATICS · Single correct · CBSE · Mathematics · Sequences and Series · Sequences and Series

Problem

If for x,y∈R,x>0x, y \in R, x > 0, y=log⁡10x+log⁡10x1/3+log⁡10x1/9+…y = \log_{10} x + \log_{10} x^{1/3} + \log_{10} x^{1/9} + \dots upto ∞\infty terms and 2+4+6+⋯+2y3+6+9+⋯+3y=4log⁡10x\frac{2+4+6+\dots+2y}{3+6+9+\dots+3y} = \frac{4}{\log_{10} x}, then the ordered pair (x,y)(x, y) is equal to: (A) (106,6)(10^6, 6) (B) (104,6)(10^4, 6) (C) (102,3)(10^2, 3) (D) (106,9)(10^6, 9)

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