Which is larger?

Geometry Level 3

A=maxxR(log23)sinx,B=maxxR(log32)sinx 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, AA or B?B?

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