perplexus.info :: Just Math : Prove irrationality

Prove irrationality (Posted on 2011-08-07)

Prove that lg(3) is irrational.

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

See The Solution Submitted by Ady TZIDON

Rating: 5.0000 (3 votes)

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Proof

| Comment 1 of 4

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.

Posted by Math Man on 2011-08-07 13:47:55

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