2022 AMC 12A Problems/Problem 14

Problem

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

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

Let $\text{log } 2 = x$ . The expression then becomes $(1+x)^3+(1-x)^3+(3x)(-2x)=\boxed{2}.$

-bluelinfish

2022 AMC 12A (Problems • Answer Key • Resources)
Preceded by Problem 13	Followed by Problem 15
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All AMC 12 Problems and Solutions