Çözüldü Exponential Expressions and Logarithm

If 2^m = 81 and 2^n = 3, what is the n / m ratio?

A) 4
B) 3
C) 1
D) 1 / 4

Güvender 1992 Matematik (Turkish)
https://yadi.sk/i/DGy-pLEwdnSdh
[Page 564 (592 in the pdf file), The Last Question, Answer: The Last Page]

Solution - 1: 2^m = 81 = 3^4 = (2^n)^4 = 2^(4n) ⇒ m = 4n ⇒ 1 / 4 = n / m.

Solution - 2:
m·log(2) = 4·log(3)....(I)
n·log(2) = log(3)....(II)
Dividing (II) by (I) yields n / m = 1 / 4.