According to Li & Vitanyi, the joint Kolmogorov complexity is\begin{align*}K(x,y) = K(x) + K(y|x) + O(\log_2(K(x,y))).\end{align*}Is it correct to say the logarithm can be dropped if we consider the equation asymptotically?  In other words, as $K(x,y)$ grows towards infinity, the logarithm becomes insignificant.
Asymptotically dropping the log in joint Kolmogorov complexity
kolmogorov complexity