Question

12<2^(m/n)<13 ..... what are the smallest possible integers for m and n?

Answer 1

its a challenging quesion...

Answer 2

positive integers?

Answer 3

n=3 and m=11 ?

Answer 4

@aceace

Answer 5

let m/n =q
=> 12 < 2^q < 13
clearly,q will be between 3 and 4
2^q = 12 shall give our ans
taking log to base 10,
q(0.3) = 2(0.3) + (0.5)
q = 11/3
so i go with @mukushla

Answer 6

wolfram tells me 3.485 approx => 697/200

Answer 7

can you please explain the log part...

Answer 8

log(2) and log(3) to base 10 are basic ones..
log2 = 0.3010
and log 3 = 0.5 approx..

Answer 9

\[12<2^{m/n}<13 \\ take \ \ \log \\ \log 12<\frac{m}{n} \log 2<\log 13 \\ \frac{\log 13}{\log 2}<\frac{m}{n} <\frac{\log 13}{\log 2}\\ 3.5<\frac{m}{n}<3.7\]

Answer 10

simply u can see m=11 and n=3 is your answer

Answer 11

how do you see that those integers are the answer?

Answer 12

how do you see that those integers are the answer?

Answer 13

how do you see that those integers are the answer?

Answer 14

how do you see that those integers are the answer?

Answer 15

how do you see that those integers are the answer?

Answer 16

how do you see that those integers are the answer?

Answer 17

how do you see that those integers are the answer?

Answer 18

note that inequality sign didnt reverse since we were taking base >1

Answer 19

yep

Answer 20

i see.. thanks