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???

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