Smeagol's Genius Game

Smeagol is a very brilliant creature! In his spare time, he figured out that $\log_35 = 1.465$ 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 $b$ such that $3^b > 5^{360}$. If Bilbo finds the correct $b$, Smeagol must lead him out of the cave. Otherwise, Bilbo becomes Smeagol's lunch. What $b$ should Bilbo choose to guarantee his safe passage out of the cave?