Question

If $m$ and $n$ are natural numbers such that $2^m-2^n=960$. Find the value of $m$?

Answer 1

$2^m-2^n$$=960$

$2^n(2^{m-n}-1)=2^6\left(15\right)$

$2^n(2^{m-n}-1)=2^6\left(15\right)$

$2^n(2^{m-n}-1)=2^6(2^4-1)$

$\Rightarrow n=6$ and $m-n=4$

$m=n+4$

$m=6+4$

$m=10$