5^x+5^(x+2)=650

=>5^x+5^x. 5^2=650

=>5^x.(1+5^2)=650

=>5^x.26=650

=>5^x=650:26

=>5^x=25

=>5^x=5^2

=>x=2

Vậy x=2

\(5^{x+2}+5^x=650\)

\(\Leftrightarrow5^x.5^2+5^x=650\)

\(\Leftrightarrow5^x\left(5^2+1\right)=650\)

\(\Leftrightarrow5^x=25=5^2\)

\(\Leftrightarrow x=2\)

[6: 3/5 - 7/6 x 6/7] : [ 21/5 x 10/11 + 57/11]

= 9 : 9

= 1 

\(\left(6:\frac{3}{5}-\frac{7}{6}\times\frac{6}{7}\right):\left(\frac{21}{5}\times\frac{10}{11}+\frac{57}{11}\right)\)

\(=\left(10-1\right):\left(\frac{42}{11}+\frac{57}{11}\right)\)

\(=9:9\)

\(=1\)

\(\left(6\div\frac{3}{5}-\frac{7}{6}\times\frac{6}{7}\right)\div\left(\frac{21}{5}\times\frac{10}{11}+\frac{57}{11}\right)\)

\(=\left(6\times\frac{5}{3}-1\right)\div\left(\frac{42}{11}+\frac{57}{11}\right)\)

\(=\frac{13}{5}\div9\)

\(=\frac{13}{45}\)

2. ( x-3 ) + 3. (x+5) > 16

x = 7/5

a)5^x +5^x+2=650

=> 5^x+5^x. 5² =650

=> 5^x(1+5²)=650

=> 5^x. 26=650

=> 5^x=25

=> x= 2

b) 3^x-1 +5 x 3 ^x-1 = 162

=> 3 ^x-1 (5 +1) = 162

=> 3 ^x-1 x 6 = 162

=> 3 ^x-1 = 27

=> x-1 =3

=> x =2

\(x^2=16\)

\(x^2=4^2\)

\(x=4\)

\(\Leftrightarrow x^2=8\cdot2=16\Leftrightarrow\left[{}\begin{matrix}x=4\\x=-4\end{matrix}\right.\)

\(5^x.5^{x+1}.5^{x+2}=5^{x+x+1+x+2}=5^{3\left(x+1\right)}\le5^{18}\)

\(\Rightarrow3\left(x+1\right)\le18\Rightarrow x+1\le6\Rightarrow x\le5\)

Đặt \(\frac{x}{5}=\frac{y}{3}=k\)

=> \(\frac{2x}{10}=\frac{3y}{9}=k\)

=> \(\orbr{\begin{cases}2x=10k\\3y=9k\end{cases}}\)

=> 2x - 3y = 10k - 9k

=> k = -6

Do đó : x = 5.(-6) = -30,y = 3.(-6) = -18

Vậy x = -30,y = -18

Thanks bạn