Question

care este mai mare 3³⁸ sau 2⁵⁷​

Answer 1

Răspuns: 3³⁸ > 2⁵⁷

$\huge {2}^{57} = {2}^{1.5 \times 38} = 2 {}^{ \frac{3}{2} \times 38 } = \\ \\ \huge =( 2 {}^{ \frac{3}{2} } ) {}^{38} = (\sqrt{2 {}^{3} } ) {}^{ 38} = \\ \\ \huge = ( \sqrt{8} ) {}^{38}$

2 ⁵⁷ = ✓8 ³⁸

3³⁸ = ( ✓3² )³⁸ = ✓9³⁸

cum 9 > 8 → 3³⁸ > 2⁵⁷