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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.