$$\lim_{x \to \infty}\left(\frac{\log{\left(3 \right)}}{\log{\left(2 \right)} \log{\left(2 x \right)} \log{\left(3 x \right)}}\right) = 0$$
$$\lim_{x \to 0^-}\left(\frac{\log{\left(3 \right)}}{\log{\left(2 \right)} \log{\left(2 x \right)} \log{\left(3 x \right)}}\right) = 0$$
Más detalles con x→0 a la izquierda$$\lim_{x \to 0^+}\left(\frac{\log{\left(3 \right)}}{\log{\left(2 \right)} \log{\left(2 x \right)} \log{\left(3 x \right)}}\right) = 0$$
Más detalles con x→0 a la derecha$$\lim_{x \to 1^-}\left(\frac{\log{\left(3 \right)}}{\log{\left(2 \right)} \log{\left(2 x \right)} \log{\left(3 x \right)}}\right) = \frac{1}{\log{\left(2 \right)}^{2}}$$
Más detalles con x→1 a la izquierda$$\lim_{x \to 1^+}\left(\frac{\log{\left(3 \right)}}{\log{\left(2 \right)} \log{\left(2 x \right)} \log{\left(3 x \right)}}\right) = \frac{1}{\log{\left(2 \right)}^{2}}$$
Más detalles con x→1 a la derecha$$\lim_{x \to -\infty}\left(\frac{\log{\left(3 \right)}}{\log{\left(2 \right)} \log{\left(2 x \right)} \log{\left(3 x \right)}}\right) = 0$$
Más detalles con x→-oo