If for $x, y \in R, x0, y=\log _{10} x+\log _{10} x^{1 / 3}+\log _{10} x^{1 / 9}+\ldots$ upto $\infty$ terms and $\frac{2+4+6+\ldots+2 y}{3+6+9+\ldots+3 y}=\frac{4}{\log _{10} x}$, then the ordered pair $(x, y)$ is equal to. [JEE Main 2021, 27 Aug (Shift 1)]

Question

If for $x, y \in R, x>0, y=\log _{10} x+\log _{10} x^{1 / 3}+\log _{10} x^{1 / 9}+\ldots$ upto $\infty$ terms and $\frac{2+4+6+\ldots+2 y}{3+6+9+\ldots+3 y}=\frac{4}{\log _{10} x}$, then the ordered pair $(x, y)$ is equal to. [JEE Main 2021, 27 Aug (Shift 1)]

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