The graph of f(x) and g(x) is defined for x>0 as logarithmic function is always defined for x>0. By looking at the attached graph of f(x)=log(7 x) and g(x)=log(4 x) we could clearly observe that
f(x) and g(x) tends to minus infinity as x tends to zero i.e. f(x)≈g(x) when x→0.
When a translation is performed on a shaped, it simply moves location. The size and shape of the object do not change. Therefore, the length of AC will remain the same at all times.