$$\lim_{x \to \infty} \log{\left(2 \right)} = \log{\left(2 \right)}$$ $$\lim_{x \to 0^-} \log{\left(2 \right)} = \log{\left(2 \right)}$$ More at x→0 from the left $$\lim_{x \to 0^+} \log{\left(2 \right)} = \log{\left(2 \right)}$$ More at x→0 from the right $$\lim_{x \to 1^-} \log{\left(2 \right)} = \log{\left(2 \right)}$$ More at x→1 from the left $$\lim_{x \to 1^+} \log{\left(2 \right)} = \log{\left(2 \right)}$$ More at x→1 from the right $$\lim_{x \to -\infty} \log{\left(2 \right)} = \log{\left(2 \right)}$$ More at x→-oo