crazy about sth that i don't know...

For natural number n and m, e^m>3, e^n>e^m then, loge(n)^n + loge(m)^m can be:
1.) 1.48 2.) 2.72 3.) 3.55 4.) 4.68 5.) 5.46
solution given
e^m>3 that means m> or = 2 as m is a natural number
e^n>e^m that means n>m i.e. n> or = 3 and n>m
the loge(n)^n+loge(m)^m> or + loge(3)^3 + loge(2)^2
=loge(27)+loge(4)
=loge(n)^n+loge(m)^m > or = loge(27*4) = loge(108)
I can understand up till here but after that the solution says
loge(108) > log3(108) > log3(81) = 4
loge(108) > 4
hence marking 4.) 4.68 why???
can't it be 5.48 5th option and how can we define the upper limit
is'nt the answer incomplete in itself???