Lời giải:

1.

$3^{x+2}+4.3^{x+1}=7.3^6$

$3^{x+1}.3+4.3^{x+1}=7.3^6$

$3^{x+1}(3+4)=7.3^6$

$3^{x+1}.7=7.3^6$

$\Rightarrow 3^{x+1}=3^6$

$\Rightarrow x+1=6$

$\Rightarrow x=5$

2.

$5^{x+4}-3.5^{x+3}=2.5^{11}$

$5^{x+3}.5-3.5^{x+3}=2.5^{11}$

$5^{x+3}(5-3)=2.5^{11}$

$2.5^{x+3}=2.5^{11}$

$\Rightarrow 5^{x+3}=5^{11}$

$\Rightarrow x+3=11$

$\Rightarrow x=8$

3.

$4^{x+3}-3.4^{x+1}=13.4^{11}$

$4^{x+1}.4^2-3.4^{x+1}=13.4^{11}$

$4^{x+1}.16-3.4^{x+1}=13.4^{11}$

$13.4^{x+1}=13.4^{11}$

$\Rightarrow 4^{x+1}=4^{11}$

$\Rightarrow x+1=11$
$\Rightarrow x=10$

\(5^{x+4}-3.5^{x+3}=2.5^{11}\)

\(5^{x+3}\left(5-3\right)=2.5^{11}\)

\(5^{x+3}.2=2.5^{11}\)

\(5^{x+3}=5^{11}\)

\(x+3=11\)

\(x=8\)

\(4^{x+3}-3.4^{x+1}=13.4^{11}\)

\(4^{x+1}\left(4^2-3\right)=13.4^{11}\)

\(4^{x+1}.13=13.4^{11}\)

\(4^{x+1}=4^{11}\)

\(x+1=11\)

\(x=10\)

\(5^{x+4}-3.5^{x+3}=2.5^{11}\)

\(5^{x+3}.5-3.5^{x+3}=2.5^{11}\)

\(5^{x+3}.\left(5-3\right)-2.5^{11}=0\)

\(5^{x+3}.2-2.5^{11}=0\)

\(2\left(5^{x+3}-5^{11}\right)=0\)

\(\Rightarrow5^{x+3}-5^{11}=0\)

\(\Rightarrow5^{x+3}=5^{11}\)

\(\Rightarrow x+3=11\)

\(\Rightarrow x=8\)

vậy \(x=8\)

sai đề rồi bạn oi 5^x+4-3.5^x+3=0 mà sao mà bằng 2.5^11được

1) Tìm số nguyên x, biết : 

a) 3^{x + 2} + 4 . 3^{x + 1} = 7.3⁶

3^{x + 1} ( 3 + 4) = 7.3⁶

3^{x + 1} .7 = 7.3⁶

=> x + 1 = 6

=> x = 5

b) 4^{x + 3} - 3.4^{x + 1} = 13 . 4¹¹

4^{x + 1} ( 4² - 3) = 13 . 4¹¹

4^{x + 1} . 13 = 13 . 4¹¹

=> x + 1 = 11

=> x = 10