For Bayes we can write
$$ p(X|Y) = \frac{p(X)\ p(Y|X)}{p(Y)} \propto p(X)\ p(Y|X) $$
in log space we can use the sum, for example when we want to calculate the maximum.
$$ argmax_k\ p(X=k|Y) = argmax_k\ \log p(X=k) + \log p(Y|X=k) $$
Question
Is there a way to formulate proportionality in log space as well?
Writing:
$$ [\log] \ \ p(X=k|Y) \propto \log p(X=k) + \log p(Y|X=k) $$
feels wrong with and without logarithm on the left side.