If sum of the first $21$ terms of the series $\log _{9^{\frac{1}{2}}} x+\log _{9^{\frac{1}{3}}} x+$ $\log _{9^{\frac{1}{4}}} x+\ldots$, where $x0$ is $504,$ then $x$ is equal to [JEE Main 2021, 20 Jul (Shift 2)]

Question

If sum of the first $21$ terms of the series $\log _{9^{\frac{1}{2}}} x+\log _{9^{\frac{1}{3}}} x+$ $\log _{9^{\frac{1}{4}}} x+\ldots$, where $x>0$ is $504,$ then $x$ is equal to [JEE Main 2021, 20 Jul (Shift 2)]

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If sum of the first \(21\) terms of the series \(\log _{9^{\frac{1}{2}}} x+\log _{9^{\frac{1}{3}}} x+\) \(\log _{9^{\fra…

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