If $l o g_{x} y = 100$ and $l o g_{2} x = 10$ , then the value of y is

2^{10}

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2^{100}

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2^{1000}

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2^{10000}

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Solution

The correct option is C $2^{1000}$
$l o g_{2} x = 10 \Rightarrow x = 2^{10}$
$∴ l o g_{x} y = 100$
$\Rightarrow y = x^{100}$
$\Rightarrow y = (2^{10})$ [put value of x]
$\Rightarrow y = 2^{1000}$

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