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Prove irrationality (Posted on 2011-08-07) Difficulty: 1 of 5
Prove that lg(3) is irrational.

Rem: lg(m)=t implies 10^t=m

  Submitted by Ady TZIDON    
Rating: 5.0000 (2 votes)
Solution: (Hide)
Proof | Comment 1 of 2 Suppose log(3) is rational. Then, for some integers x and y, log(3)=x/y. Here is what we get. ylog(3)=x 10^(ylog(3))=10^x 3^y=10^x However, all powers of 3 are odd, and powers of 10 are even. Therefore, log(3) is irrational.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
Some Thoughtsre: Proof......kudosAdy TZIDON2011-08-07 14:58:35
SolutionProofMath Man2011-08-07 13:47:55
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