2 ) So sánh 333^444 và 444^333: 
Có 333^444=(333^4)^111 và 444^333=(444^3)^111 
Như vậy ta cần so sánh 333^4 và 444^3: 
Vì 333^4/444^3=3^4*111^4/(4^3*111^3)=3^4*11... nên 333^4>444^3 do đó 
333^444>444^333 

1,\(\frac{2}{3}x=\frac{3}{4}y=\frac{4}{5}z\Rightarrow\frac{12x}{18}=\frac{12y}{16}=\frac{12z}{15}\)

Aps dụng tính chất dãy tỉ số bằng nhau, ta có:

\(\frac{12x}{18}=\frac{12y}{16}=\frac{12z}{15}=\frac{12x+12y+12z}{18+16+15}=\frac{12\left(x+y+z\right)}{49}=\frac{12.147}{49}=\frac{1764}{49}\)=36

\(\Rightarrow\hept{\begin{cases}x=36.18:12=54\\y=36.16:12=48\\z=36.15:12=45\end{cases}}\)

Vậy:.......

1.

Đặt \(\frac{2}{3}x=\frac{3}{4}y=\frac{4}{5}z=k\)    \(\Leftrightarrow\hept{\begin{cases}x=\frac{3}{2}k\\y=\frac{4}{3}k\\z=\frac{5}{4}k\end{cases}}\)

mà \(x+y+z=147\) \(\Leftrightarrow\frac{3}{2}k+\frac{4}{3}k+\frac{5}{4}k=147\) \(\Leftrightarrow k\left(\frac{3}{2}+\frac{4}{3}+\frac{5}{4}\right)=147\)

\(\Leftrightarrow\frac{49}{12}k=147\) \(\Leftrightarrow k=147\div\frac{49}{12}=36\)

\(\Leftrightarrow\hept{\begin{cases}x=\frac{3}{2}k=54\\y=\frac{4}{3}k=48\\z=\frac{5}{4}k=45\end{cases}}\)

2.

\(\left(3^4\right)^{111}\times111^{111}>\left(4^3\right)^{111}\)\(\Leftrightarrow3^{444}\times111^{111}\times\left(111^{111}\right)^4>4^{333}\times\left(111^{111}\right)^3\) 

\(\Leftrightarrow3^{444}\times111^{444}>4^{333}\times111^{333}\)

\(\Leftrightarrow333^{444}>444^{333}\)

\(\frac{x-1}{27}=\frac{-3}{1-x}\)

\(\Rightarrow\frac{x-1}{27}=\frac{3}{x-1}\)

\(\Rightarrow\left(x-1\right)^2=81\)

\(\Rightarrow x-1=\pm9\)

Làm nốt nhassssso

so sánh 

ta có 

333⁴⁴⁴=333^4.111=(333⁴)¹¹¹

444³³³=444^3.111=(444³)¹¹¹

So sánh 333⁴và 444³ ta có 

333⁴=(3.111)⁴=3⁴ . 111⁴=81.111⁴

444³=(4.111)³=4³. 111³=64. 111³

Vì 81.111⁴>64.111³

Suy ra 333⁴⁴⁴>444³³³