Answers

  • Brainly User
2015-08-23T15:05:05+05:30
Assume that log 2 is rational, that is,
log2=p/q
where p, q are integers. Since log 1=0 and log10=1,0<log2<1  and p<q.
2=10^p/q
2^p=(2*5)^q
2^q-p=5^p
where q – p is an integer greater than 0.Now, it can be seen that the L.H.S. is even and the R.H.S. is odd. Hence there is contradiction and  log 2  is irrational. 
5 2 5