Log 2 is rational or irrational ? Justify your answer
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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.
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