Proof that Log2 of 5 is irrational

  • #1

Homework Statement



Prove that log2 of 5 is irrational.

Homework Equations



None.

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.
 

Answers and Replies

  • #2
291
0
[tex]\log_2 5 = a/b[/tex] so [tex]2^{a/b} = 5 \implies 2^a = 5^b[/tex]. Now use unique factorization.
 
  • #3
[tex]\log_2 5 = a/b[/tex] so [tex]2^{a/b} = 5 \implies 2^a = 5^b[/tex]. Now use unique factorization.

But does mine work?
 
  • #4
rock.freak667
Homework Helper
6,223
31
[tex]\log_2 5 = a/b[/tex] so [tex]2^{a/b} = 5 \implies 2^a = 5^b[/tex]. Now use unique factorization.

What is unique factorization ?
 

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