Question

5^45 comparat la 4^60​

Answer 1

Răspuns:

5⁴⁵=(5³)¹⁵=125¹⁵

4⁶⁰=(4⁴)¹⁵=256¹⁵

avem acelasi exponent comparam bazele

125 < 256

5⁴⁵ < 4⁶⁰

Answer 2

Răspuns: $\boxed{5^{45} \;\;<\;\;4^{60}}$

Explicație pas cu pas:

$5^{45} = 5^{3\cdot 15} = (5^{3})^{15} =\boxed{ 125^{15} }$

$4^{60} = 4^{4\cdot 15} = (4^{4})^{15} =\boxed{\: 256^{15}\: }$

$125^{15} \;\;<\;\;256^{15}$

$\boxed{5^{45} \;\;<\;\;4^{60}}$