Which is larger?

Geometry Level 3

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

\[\text{ Which is larger : } A \text{ or } B \ ? \]

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