1. ## Indices

HI. I am having trouble with this question.

Find the smallest positive integers m and n for which:

a) $12< 2^{m/n}< 13$

b) $13< 2^{m/n}< 14$

Thanks

2. Originally Posted by deltaxray
HI. I am having trouble with this question.

Find the smallest positive integers m and n for which:

a) $12< 2^{m/n}< 13$

b) $13< 2^{m/n}< 14$

Thanks
a) 2^11/2

b) 2^15/4
I hope that helps.

3. @Awsom Guy :

$2^{\frac{ 11}{2}} = 2^{5.5} \approx 45$

The second one seems right though. Anyway, a more "algebraic" answer :

$12 < 2^{m/n} < 13$

$log_2(12) < log_2(2^{m/n}) < log_2(13)$

$log_2(12) < m/n < log_2(13)$

Might make it a bit easier ? (same thing for the other one)