Inclined asymptote can be found by calculating the limit of log(1/2)*x + 2, divided by x at x->+oo and x ->-oo
$$\lim_{x \to -\infty}\left(\frac{x \log{\left(\frac{1}{2} \right)} + 2}{x}\right) = - \log{\left(2 \right)}$$
Let's take the limitso,
inclined asymptote equation on the left:
$$y = - x \log{\left(2 \right)}$$
$$\lim_{x \to \infty}\left(\frac{x \log{\left(\frac{1}{2} \right)} + 2}{x}\right) = - \log{\left(2 \right)}$$
Let's take the limitso,
inclined asymptote equation on the right:
$$y = - x \log{\left(2 \right)}$$