Smeagol's Genius Game

Smeagol is a very brilliant creature! In his spare time, he figured out that log35=1.465\log_35 = 1.465 without any calculators! With this brilliant knowledge, he decided to play a "game" with Bilbo Baggins, who is lost in Smeagol's cave. In this "game", Bilbo has to find the smallest bb such that 3b>53603^b > 5^{360}. If Bilbo finds the correct bb, Smeagol must lead him out of the cave. Otherwise, Bilbo becomes Smeagol's lunch. What bb should Bilbo choose to guarantee his safe passage out of the cave?

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