Question

[Linh Ivone]

hic cho tui hỏi tý

so sánh

444⁵⁵⁵ và 555⁴⁴⁴

^{ai yêu linh ( ivone ) thì kb nha ( cả lime nữa )}

Answer 1

[Phạm Tuấn Đạt]

Ta xét :

\(444^{555}=\left(444^5\right)^{111}=\left(111^5.4^5\right)^{111}=\left(111^5.1024\right)^{111}\)

\(555^{444}=\left(555^4\right)^{111}=\left(111^4.5^4\right)^{111}=\left(111^4.625\right)^{111}\)

Mà \(111^5.1024>111^4.625\)

\(\Rightarrow444^{555}>555^{444}\)

Answer 2

[kudo shinichi]

ta có: \(444^{555}=444^{\left(111\times5\right)}=\left(444^5\right)^{111}\)

\(555^{444}=555^{\left(111\times4\right)}=\left(555^4\right)^{111}\)

ta có:  \(444^5=\left(4\times111\right)^5=4^5\times111^5\)= \(1024\times111\times111^4\)

            \(555^4=\left(5\times111\right)^4=5^4\times111^4\) = \(625\times111^4\)

ta có: \(1024\times111\times111^4\) > \(625\times111^4\)

   \(\Rightarrow\)\(444^5>555^4\)

mình làm hơi tắt bạn tự hoàn thiện nha.