Which is larger?

Geometry Level 3

A=max⁡x∈R(log⁡23)sin⁡x,B=max⁡x∈R(log⁡32)sin⁡x 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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Calvin Lin by Calvin Lin
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