If sum of the first 21 terms of the series \({\log }_{{9}^{1/2}}\text{x}+{\log }_{{9}^{1/3}}\text{x}+{\log }_{{9}^{1/4}}\text{x}+\ldots \ldots ,\) where \(x>0\) 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 \({\log }_{{9}^{1/2}}\text{x}+{\log }_{{9}^{1/3}}\text{x}+{\log }_{{9}^{1/4}}\text{x}+\ldots \ldots ,\) 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}^{1/2}}\text{x}+{\log }_{{9}^{1/3}}\text{x}+{\log }_{{9}^{1/4}}…

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