Câu hỏi của Huyền Diệu

Question

So sánh hai lũy thừa:

a/ 63¹⁵và 34¹⁸

b/ 83⁹ và 26¹²

Nguyễn Thanh Hằng · Accepted Answer

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

Câu trả lời:

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