Column A will be greater because 19 is being multiplied 20 times whereas 20 is being multiplies only 19 times.
This is similar to the question: Compare: 3⁵ 5≥; 3⁵ > 5≥
I will provide a general way to solve this type of questions:
You are comparing a^b to c^d
a^b : c^d
Ln(a^b) : Ln( c^d)
b Ln a : d Ln c
b/Ln c : d / Ln a
Whatever a,b,c, and d are, keep in mind this inequality:
x/Lnx > y/lny if x > y > 2.71 which is e
x/Lnx < y/lny if 2.71 > x > y > 0
x/Lnx < y/lny if 2.71 > x > y > 1
For this problem, 20 and 19 are both > 2.71 so the problem is easy.
19^20 : 20^19
20 Ln 19 : 19 Ln 20
20/Ln20 : 19/Ln19
A for sure.
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