\(\frac{x}{2}=\frac{y}{3}=>\frac{x}{2.4}=\frac{y}{3.4}=\frac{x}{8}=\frac{y}{12}\)

\(\frac{y}{4}=\frac{z}{7}=>\frac{y}{4.3}=\frac{z}{7.3}=\frac{y}{12}=\frac{z}{21}\)

\(=>\frac{x}{8}=\frac{y}{12}=\frac{z}{21}\)

Áp dụng tính chất dãy tỉ số bằng nhau ta có:

\(\frac{x}{8}=\frac{y}{12}=\frac{z}{21}=\frac{2x-y+z}{2.8-12+21}=\frac{50}{25}=2\)

\(=>\frac{x}{8}=2=>x=2.8=16\)

\(\frac{y}{12}=2=>y=14\)

\(\frac{z}{21}=2=>z=42\)

Vậy :x=16,y=14,z=21

Ta có :

\(\hept{\begin{cases}\frac{x}{2}=\frac{y}{3}\\\frac{y4}{7}=\frac{z}{7}\end{cases}}\Rightarrow\hept{\begin{cases}\frac{x}{8}=\frac{y}{12}\\\frac{y}{12}=\frac{z}{21}\end{cases}}\)\(\Rightarrow\frac{x}{8}=\frac{y}{12}=\frac{z}{21}\)

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

\(\frac{x}{8}=\frac{y}{12}=\frac{z}{21}=\frac{2x}{16}=\frac{2x-y+z}{16-12+21}=\frac{50}{25}=2\)

\(\Rightarrow\hept{\begin{cases}x=2.8=16\\y=2.12=24\\z=2.21=42\end{cases}}\)

3 . 5^x+1 = 75

=> 5^x+1 = 75 : 3 = 25

=> 5^x+1 = 5² 

=> x + 1 = 2

=> x = 1

ok chưa bạn

\(\frac{4}{7}+\frac{3}{7}\cdot\left|1-\frac{2}{3}x\right|=\frac{11}{14}\) \(\Rightarrow\frac{3}{7}\cdot\left|1-\frac{2}{3}x\right|=\frac{3}{14}\) \(\Rightarrow\left|1-\frac{2}{3}x\right|=\frac{1}{2}\)

\(\Rightarrow\orbr{\begin{cases}1-\frac{2}{3}x=\frac{1}{2}\\1-\frac{2}{3}x=-\frac{1}{2}\end{cases}}\) \(\Rightarrow\orbr{\begin{cases}\frac{2}{3}x=\frac{1}{2}\\\frac{2}{3}x=\frac{3}{2}\end{cases}}\) \(\Rightarrow\orbr{\begin{cases}x=\frac{3}{4}\\x=\frac{9}{4}\end{cases}}\)