WAEC Further Mathematics 2013 Paper

Concept:Use the laws of logarithms. Write each fraction as a power of $2$. Then use the power rule: $\log a^n = n\log a$.Explanation:Start with the given expression: $\log\frac{1}{8} + \log\frac{1}{2}$.Rewrite $\frac{1}{8}$ and $\frac{1}{2}$ as negative powers of $2$.Since $8 = 2^3$, we have $\frac{1}{8} = 2^{-3}$.Since $2 = 2^1$, we have $\frac{1}{2} = 2^{-1}$.Therefore, $\log\frac{1}{8} + \log\frac{1}{2} = \log 2^{-3} + \log 2^{-1}$.Apply the power rule of logarithms: $\log 2^{-3} = -3\log 2$ and $\log 2^{-1} = -\log 2$.Add the results: $-3\log 2 + (-\log 2) = -4\log 2$.The expression is now written in terms of $\log 2$.Answer:$-4\log 2$So the correct option is D. $-4\log 2$.