NIELIT 2017 DEC Scientific Assistant A - Section A: 36

Question

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

• A. $2^{10}$
• B. $2^{100}$
• C. $2^{1000}$
• D. $2^{10000}$

Answer 1

Option C is correct.

Answer 2

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 $(C).$