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<1and 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 andlog 2is irrational.