34x-2=9loga(27)=loga(279)=loga((33)9)=loga(327).
If a=3, log3(327)=27=33.
34x-2=33, so 4x-2=3, 4x=5, x=5/4.
If a≠3, then note that loga(3)log3(a)=1, loga(3)=1/log3(a), so loga(327)=27loga(3)=27/log3(a).
34x-2=27/log3(a), so, taking logs to base 3 of each side:
4x-2=log3[27/log3(a)]=log3(27)-log3(log3(a)), x=¼(5-log3(log3(a))). When a=3, log3(a)=1 and log(1)=0 for any base.
Therefore if a=9, x=¼(5-log3(log3(9)))=1.25-log3(2)/4=1.25-0.6309/4=1.0923 approx.