Math Gold Medalist

Lor

2022 AMC 12A 

Problem 14

What is the value of\[(\log 5)^3+(\log 20)^3+(\log 8)(\log 0.25)\]where $\log$ denotes the base-ten logarithm?

$\textbf{(A) } \frac{3}{2} \qquad \textbf{(B) } \frac{7}{4} \qquad \textbf{(C) } 2 \qquad \textbf{(D) } \frac{9}{4} \qquad \textbf{(E) } 3$

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   Solution