Question

prove that log 2 is irrational

Answer 1

ASSUME THAT LOG 2 IS RATIONAL, THAT IS 
LOG 2=P/Q                                                                            ......(1)
WHERE P,Q ARE INTEGERS 
SINCE LOG 1=10 AND LOG 10 =1,
0<LOG 2<1 AND THEREFORE P<Q
2=10P/Q                                                                                     (FROM 1)
2Q= (2*5)P
2Q-P= 5P
NOW IT CAN BE SEEN THAT L.H.S IS EVEN AND R.H.S IS ODD 
HENCE THERE IS A CONTRADICTION AND LOG 2 IS IRRATIONAL