HI. I am having trouble with this question.
Find the smallest positive integers m and n for which:
a) $\displaystyle 12< 2^{m/n}< 13$
b) $\displaystyle 13< 2^{m/n}< 14$
Thanks
@Awsom Guy :
$\displaystyle 2^{\frac{ 11}{2}} = 2^{5.5} \approx 45$
The second one seems right though. Anyway, a more "algebraic" answer :
$\displaystyle 12 < 2^{m/n} < 13$
$\displaystyle log_2(12) < log_2(2^{m/n}) < log_2(13)$
$\displaystyle log_2(12) < m/n < log_2(13)$
Might make it a bit easier ? (same thing for the other one)