In the proof of the Cramer-Shoup public key scheme [1], I understand that the adversary's view can be seen as equations such as $\log c = x_1 + w x_2, \log d = y_1 + w y_2$ and so on (equation 1 and 2 in [1]), where $\log = \log_{g_1}$ and $w = \log g_2$. Does this mean the adversary knows how to solve discrete log? If that's the case, why is it a reasonable assumption? Otherwise, how does the adversary know $\log c$, $\log d$ and $w$?
[1] https://link.springer.com/content/pdf/10.1007%2FBFb0055717.pdf