If the sum of the first $20$ terms of the series $ \log _{\left(7^{1 / 2}\right)} x+\log _{\left(7^{1 / 3}\right)} x+\log _{\left(7^{1 / 4}\right)} x+\ldots $ is $460$ , then $x$ is equal to [JEE Main 2020, 5 Sep (Shift 2)]

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If the sum of the first \(20\) terms of the series \( \log _{\left(7^{1 / 2}\right)} x+\log _{\left(7^{1 / 3}\right)} x+…

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