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

Submitted by Ady TZIDON

Rating: 5.0000 (3 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
Puzzle Solution	K Sengupta	2023-07-14 00:30:10
good	Victor Patrick	2023-07-13 21:13:32
re: Proof......kudos	Ady TZIDON	2011-08-07 14:58:35
Proof	Math Man	2011-08-07 13:47:55

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