Which is larger?

Geometry Level 3

\[ A = \max_{x \in \mathbb{R}} \left( \log_2 3 \right)^{\sin x }, \qquad B = \max_{x \in \mathbb{R}} \left( \log_3 2 \right)^{\sin x }\]

Which is larger, \(A\) or \(B?\)

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