mr.habibbi
Member
- Joined
- Oct 27, 2019
- Messages
- 41
- Gender
- Male
- HSC
- 2021
thanks for the suggestion but your question shows an odd and even value 10 and 5, the question i uploaded shows 5 and 13 where they are both odd.Hey, here is an example of the same question, the difference being the need to prove instead of . Working out may vary, but I thought I'd include this so you might gain an idea of how to approach your question.
View attachment 32250
View attachment 32251
I hope this helps!
Hmmm a slight modification to the blue underlined statement to account for all log irrationalities would be the following:thanks for the suggestion but your question shows an odd and even value 10 and 5, the question i uploaded shows 5 and 13 where they are both odd.
would proving ln2 irrational be the same?Expanding slightly, you can go from where and are integers and where seeking integers and straight to there being a contradiction if:
So, if I was asked for is irrational, I could get the contradiction from as 9 and 17 are co-prime. Alternatively, I could re-write 9 as 3^{2} to get . However, getting the result from co-primes is necessary in some cases, such as proving that is irrational.
- one of and is odd and the other is even, as does the proof above
- and are both prime
- and are co-prime, which means that they have no common factor except 1 - which covers many of the cases under 1 and 2 as well
I actually don't think you can prove ln(2) being irrational with the exact layout used in ext2 because ln is basically log(e) where e is a transcendental number (i.e. not an integer) so dont worry too much about.would proving ln2 irrational be the same?