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29^{200} 2^{151} ? 5^{279} 3^{300} (V Soros Olympiad 1998-99 Round 3 10.3)

Source:

May 26, 2024

algebra

Problem Statement

Without using a calculator, find out which number is greater:

29^{200}\cdot 2^{151} \,\,\, or \,\,\, 5^{279} \cdot 3^{300}