Smeagol's Genius Game

Number Theory Level 2

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?

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Smeagol's Genius Game

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, interactive explorations.

Used and loved by over 6 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.