log4⁡18 is

Let log4⁡18=p/q, where p,q∈I⇒ log4⁡9+log4⁡2=pq⇒ 12×2log2⁡3+12=pq⇒ log2⁡3=pq−12=mn( say ) where m,n∈I and n≠0⇒ 3=(2)m/n or 3n=2m (possible only when m=n=0 which is not true) Hence, log4⁡18  is an irrational number.