math question on naive bayes

Hello,
i read on a paper "nayve bayes filtering using Word-position-based
Attributes" that I can choose if a mail is spam or not:

if P(ham|d)/P(spam|d) > lamba (with lambda>1)
then is Spam. OK.

What about if I change the original formula using the
log trick:
nvb = argmax log (nayve bayes forumula for classification)

Must I do this:
P(ham|d)/P(spam|d) > log (lamba)

I don't think the latter. How can I change the formula? I'd like use lambda because in this way I can do some experiment for lambda equal to 1, 10, 100.

thanks in advance,