Question

If $lo{g}_{x}y=100$ and $lo{g}_{2}x=10$, then the value of y is

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

Answer 1

The correct option is C

$2^{1000}$

Given that,

$lo{g}_{2}x=10\iff x=2^{10}$ [$\because lo{g}_{b}a=x$ implies $a=b^x$]

$lo{g}_{x}y=100\iff x^{100}=y$

$\Rightarrow (2^{10}{)}^{100}=y$

$\Rightarrow 2^{1000}=y$