2^x+2.3^x=12^x

=> 2^x+2.3^x=(4.3)^x

=> 2^x+2.3^x=4^x.3^x

=> 2^x+2=4^x

=> 2^x+2=(2²)^x=2^2x

=> x+2=2x

=> 2=2x-x

=> x=2

`(3*x+2)^2=121`

\(=>\left[{}\begin{matrix}3x+2=11\\3x+2=-11\end{matrix}\right.\\ =>\left[{}\begin{matrix}3x=11-2\\3x=-11-2\end{matrix}\right.\\ =>\left[{}\begin{matrix}3x=9\\3x=-13\end{matrix}\right.\\ =>\left[{}\begin{matrix}x=3\left(tm\right)\\x=-\dfrac{13}{3}\left(loại\right)\end{matrix}\right.\)

`(3x+2)^2=121`

`=>( 3x+2)^2= +-11^2`

\(\Rightarrow\left[{}\begin{matrix}3x+2=11\\3x+2=-11\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}3x=9\\3x=-13\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=3\\x=-\dfrac{13}{3}\end{matrix}\right.\)

2/x + y/3 = 2

=> 2/x = 2 - y/3

= 2/x = 6-y/3

=> x(6-y) = 2.3

x(6-y) = 6

Do x∈N => x >= 0. Để x(6-y) = 6 thì x > 0

Mà 6>0 => 6-y > 0

Mà y∈ N => 6-y ∈ N*

Ta có bảng:

Thử lại thỏa mãn.

Vậy (x,y) = (1,0); (2,3); (3,4); (6,5)

câu 1 = 0 
câu 2 = 3 
câu 3 k rõ 
câu 4 từ từ

|x + 2| = |x - 2|

=> x + 2 = x - 2

x - x = -2 - 2

0 = -4 (vô lí)

hoặc x + 2 = -x + 2

x + x = 2 - 2

2x = 0

x = 0

Vậy x = 0

-3^x = -27

-3^x = -3³

<=> x = 3

|x + 2| = |x - 2|

=> x + 2 = x - 2 hoặc x + 2 = 2 - x

+) x + 2 = x - 2

=> x - x = -2 - 2

=> 0 = -4 (vô lý)

+) x + 2 = 2 - x

=> x + x = 2 - 2

=> 2x = 0

=> x = 0

Vậy x = 0

2.3^x+3^x+2=99.3^12

3^x.(2+3^2)=9.11.3^12

3^x.11=11.3^12.3^2

3^x=3^14

=>x=14

**** nhe