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Proof that Log2 of 5 is irrational

  1. Nov 24, 2007 #1
    1. The problem statement, all variables and given/known data

    Prove that log2 of 5 is irrational.

    2. Relevant equations

    None.

    3. The attempt at a solution

    I just had a glimpse of the actual solution, but I'm wondering if mine would work too.

    2^(a/b) = 5

    square both sides...

    2^(2a/b) =25

    2 = 25^(b/2a)

    (b/2a) = log25 of 2

    b = 2aLog25 of 2

    b is even...

    and through a similar process...by taking the square root of both sides of "2^(a/b) = 5" you can arrive at a being even too. So how can they both be even etc etc.
     
  2. jcsd
  3. Nov 24, 2007 #2
    [tex]\log_2 5 = a/b[/tex] so [tex]2^{a/b} = 5 \implies 2^a = 5^b[/tex]. Now use unique factorization.
     
  4. Nov 24, 2007 #3
    But does mine work?
     
  5. Nov 24, 2007 #4

    rock.freak667

    User Avatar
    Homework Helper

    What is unique factorization ?
     
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