Question

5. Comparați numerele a = 5¹⁸ și b= 15¹²​

Answer 1

Răspuns:

Explicație pas cu pas:

a=5¹⁸=(5³)⁶=125⁶

b=(15²)⁶=225⁶

125⁶<225⁶

a<b

5¹⁸<15¹²

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Answer 2

$\it\dfrac{5^{18}}{15^{12}}=\dfrac{5^6\cdot5^{12}}{3^{12}\cdot5^{12}}=\dfrac{5^6}{3^{12}}=\dfrac{5^6}{(3^2)^6}=\dfrac{5^6}{9^6}=\Big(\dfrac{5}{9}\Big)^6 < 1 \Rightarrow5^{18} < 15^{12}$