2log ( a - 2b) = log a + log b
log (a - 2b)^2 = log (ab) this implies that
(a - 2b)^2 = ab
a^2 - 4ab + 4b^2 = ab
a^2 - 5ab + 4b^2 = 0 factor
(a - 4b) (a - b) = 0
So either
a - 4b = 0 or a - b = 0
a = 4b a = b
a/b = 4 a/b = 1
But the second solution means that we are taking the log of a negative number at some point
So
a/b = 4