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# C3 solomon paper, no clue what to do watch

(b) Use proof by contradiction to prove that log2 3 is irrational. (6)
Never seen it before any explanations would be greatly appreciated!
2. (Original post by Icyytea)
(b) Use proof by contradiction to prove that log2 3 is irrational. (6)
Never seen it before any explanations would be greatly appreciated!
start by assuming it is true, so log(base2)3 = p/q where p and q are rational numbers
3. You know that logab = c means ac = b so go from there
4. I get 2^(p/q) = 3 now i'm lost, i've never done this before
is it even c3?
5. (Original post by Icyytea)
I get 2^(p/q) = 3 now i'm lost, i've never done this before
is it even c3?
Try rearranging. Write 2^(p/q) as (2^p)^(1/q)=3 and then rearrange further.
6. (Original post by ViralJZ)
Try rearranging. Write 2^(p/q) as (2^p)^(1/q)=3 and then rearrange further.
ah i see and then since q/p are rational they must both be integers but for any integers the 2^p = 3^q equation isn't true?
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7. (Original post by Icyytea)
ah i see and then since q/p are rational they must both be integers but for any integers the 2^p = 3^q equation isn't true?
Indeed. 2^p where p is an integer is always an even number multiplied by an even number. 3^q where q is an integer is always an odd number multiplied by an odd number.
8. Awesome guys thanks

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