Question:

Key Concept: $\log_4 256 = \log_4 4^4 = 4$. $\log_2(\log_2 4) = \log_2 2 = 1$. $\log_{\sqrt{2}} 2 = \log_{\sqrt{2}}(\sqrt{2})^2 = 2$. So $A = 1 + \dots$ wait: $\log_2(\log_2 4) = \log_2 2 = 1$, then $\log_2(1) = 0$, plus $\log_{\sqrt{2}} 2 = 2$. Recheck: $\log_2 256 = 8$; $\log_4 256 = 4$; $\log_2 4 = 2$; $\log_2 2 = 1$. Chain: $A = \log_2(\log_2 4) + 2 = \log_2 2 + 2 = 1 + 4 = 5$. Wait: $\log_2(\log_2(\log_4 256)) = \log_2(\log_2(4)) = \log_2(2) = 1$. Then $A = 1 + \log_{\sqrt{2}} 2 = 1 + 2 = 3$.