Logarithms Practice Test 2

Concept:Nested logarithms are evaluated from the innermost bracket outward.Use the change of base rule for logs with unusual bases.Explanation:First simplify the innermost log:$\log_4 256 = \log_4 4^4 = 4$.Next evaluate the middle log:$\log_2 4 = \log_2 2^2 = 2$.Then the outermost log:$\log_2 2 = 1$.So the nested log part equals $1$.Now evaluate the second term:$2\log_{\sqrt{2}} 2$.Using change of base:$\log_{\sqrt{2}} 2 = \frac{\log_2 2}{\log_2 \sqrt{2}} = \frac{1}{\frac{1}{2}} = 2$.Therefore $2 \times 2 = 4$.Finally add the two parts:$A = 1 + 4 = 5$.Answer:$A = 5$, so the correct option is C.