Prove that lg(3) is irrational.
Rem: lg(m)=t implies 10^t=m
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 20110807 13:47:55 