Question

Given that $2^n\times 2^3=2^9$, find the value of $n$.

• A. $3$
• B. $6$
• C. $8$
• D. $12$

Answer 1

The correct option is B $6$

$2^n\times 2^3=2^9$

$\Rightarrow 2^n=\frac{2^9}{2^3}$

$\Rightarrow 2^n=2^6$

$\Rightarrow {\log }_2\left(2^n\right)={\log }_2\left(2^6\right)$

$\Rightarrow n{\log }_{2}2=6{\log }_{2}2$

$\Rightarrow n=6$