NIELIT 2017 DEC Scientific Assistant A - Section A: 36

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If $\log_{x}y=100$ and $\log_{2}x=10$, then the value of $y$ is :

1. $2^{10}$
2. $2^{100}$
3. $2^{1000}$
4. $2^{10000}$

Option C is correct.

Given that, $\log_{x}y = 100$ and $\log_{2}x = 10$

$\implies \dfrac{\log_{2}y}{\log_{2}x} = 100$

$\implies \dfrac{\log_{2}y}{10} = 100$

$\implies \log_{2}y = 1000$

$\implies y = 2^{1000}.$

So, the correct answer is $(C).$
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