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

460 = _7 x ( 2 + 3 + 4 + + 20 + 21 ) \\ 460 = _7 x ( 21 222 - 1 ) \\ 460 = 230 _7 x \\ _7 x = 2 x = 7^2</

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: 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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