Note that a, b are both positive
Using some log properties
log ( a - 2b)^2 = log (a * b)
This means that
(a - 2b)^2 = ab
a^2 - 5ab + 4b^2 = 0
(a - 4b) ( a - b) = 0
Either
a - b= 0
a = b
a / b = 1 { this may produce a log of a negative - not allowed }
Or
a - 4b = 0
a = 4b
a / b = 4
The second is correct