4: The given limit is one-sided, so we only use x > 0.

For a > 0 we have a⋅x + 1 > 1 and the logarithm is positive. Thus we get a "positive zero" in the denominator.

For a < 0 we have a⋅x + 1 < 1 and the logarithm is negative. Thus we get a "negative zero" in the denominator.

Answer