Răspuns: 2^111 × 5^38 < 3^131
Explicație pas cu pas:
2^111 x 5^38 = (2^3)^37 x (5^2)^19 = 8^37 x 25^19
3^131 = 3^57 x 3^74 = (3^3)^19 × (3^2)^37 = 27^19 × 9^37
25^19 < 27^19
8^37 < 9^37
25^19 x 8^37 < 27 ^19 x 9^37
2^111 × 5^38 < 3^131
2¹¹¹×5³⁸ = (2³)³⁷×(5²)¹⁹ = 8³⁷×25¹⁹
3¹³¹ = 3⁷⁴×3⁵⁷ = (3²)³⁷×(3³)¹⁹ = 9³⁷×27¹⁹
Comparam
8³⁷ < 9³⁷
25¹⁹ < 27¹⁹ } => 8³⁷×25¹⁹ < 9³⁷×27¹⁹ => 2¹¹¹×5³⁸ < 3¹³¹
