If the sum of the first 20 terms of the series log _( 7^1/2 )x + log _( 7^1/3 )x + log _( 7^1/4 )x + ... is 460 , then x is equal to

460 = log _7 x ( 2 + 3 + 4 + * s + 20 + 21 ) \ => 460 = log _7 x ( (21 * 22 / 2) - 1 ) \ => 460 = 230 log _7 x \ => log _7 x = 2 => x = 7^2

If the sum of the first 20 terms of the series \log_{... | Sequence & Series (Mathematics)

460 = $\log_{7} x \left( 2 + 3 + 4 + \cdots + 20 + 21 \right)$ $\\ \Rightarrow 460 = \log_{7} x \left( \frac{21 \cdot 22}{2} - 1 \right)$ $\\ \Rightarrow 460 = 230 \log_{7} x$ $\\ \Rightarrow \log_{7} x = 2$ $\Rightarrow x = 7^2$

Explanation

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