Question

If $x$ and $n$ are both positive integers, such that $4^x\times n^2=4^{x+1}$, then what is the value of $n$?

• A. $2$
• B. $4$
• C. $6$
• D. $8$

Answer 1

The correct option is A $2$

Given, $4^x\times n^2=4^{x+1}$

$\Rightarrow 4^x\times n^2=4^x{.4}^1=4^x.4$

Since $x$ is a positive integer, we can divide both sides by $4^x$, and get $n^2=4$

$\Rightarrow n=\pm 2$

SInce $n$ is also a positive integer, $n=2$

Hence, option $A$ is correct.