HMMT 2014 A3

Let

$A=\frac{1}{6}\left(\left(\log _{2}(3)\right)^{3}-\left(\log _{2}(6)\right)^{3}-\left(\log _{2}(12)\right)^{3}+\left(\log _{2}(24)\right)^{3}\right)$

Compute $2^{A}$ .

Dataset text NuminaMath olympiads. Quoted with source.

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