Suppose that log27 is rational number.∴ Let log27, where p, q ∈ N.log27.Obviously (1) is false, as the L.H.S. is odd while the R.H.S. is even and the two cannot be equal.Thus,log27 is not a rational number. Also log27 is not an integer and so it cannot be a prime number.Hence, log27 is an irrational number.