Question

So sánh hai lũy thừa:

a/ 63¹⁵ và 34¹⁸

b/ 83⁹ và 26¹²

Answer 1

a/ \(63^{15}< 64^{15}=\left(2^6\right)^{15}=2^{90}\left(1\right)\)

\(34^{18}=\left(2^5\right)^{18}=2^{90}\left(2\right)\)

Từ \(\left(1\right)+\left(2\right)\Leftrightarrow63^{15}< 34^{18}\)

b/ \(83^9>81^9=\left(3^3\right)^9=3^{27}\left(1\right)\)

\(26^{12}< 27^{12}=\left(3^3\right)^{12}=3^{36}\left(2\right)\)

Từ \(\left(1\right)+\left(2\right)\Leftrightarrow83^9< 26^{12}\)