navreetraaj
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
Answers & Comments
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