Question

Given that $n$ and $k$ are positive integers and $8^n=2^k$, then the value of $\frac{n}{k}$ is:

• A. $\frac{1}{4}$
• B. $\frac{1}{3}$
• C. $\frac{1}{2}$
• D. $3$
• E. $4$

Answer 1

The correct option is B $\frac{1}{3}$

Given, $8^n=2^k$

$\Rightarrow (2^3{)}^n=2^k$

$\Rightarrow 2^{3n}=2^k$

Since base is same

$\Rightarrow 3n=k$

$\Rightarrow \frac{n}{k}=\frac{1}{3}$