Balls are fake

Logic Level 3

A shop was delivering \(3^{15}-2\) balls. Some children placed a fake ball, perfectly identical to the original balls which is heavier than original ones. Authorities came to know it and brought an accurate weighing scale on which load is placed on both sides. So how many minimum number of trials are required to identify the fake ball?

16 17 13 \[\frac{3^{15}-1}{2}\] 14 3 15 2

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