\(2^{x+3}.2^x=144\)
\(2^{x+3+x}=2^4.3^2\)
\(2^{2x+3}=2^4.3^2\)
\(2^{2x+3-4}=3^2\)
 

`2^(x+3)+2^x=144`

`2^x *2^3 +2^x =144`

`2^x (8+1)=144`

`2^x *9=144`

`2^x =16`

`2^x =16`

`2^x =2^4`

`=>x=4`

2\(^{x+3}\)  + 2\(^x\) = 144

2\(^x\).( 2³ + 1) = 144

2^\(x\)(8 + 1) = 144

2\(^x\) . 9 = 144

2\(^x\)       = 144 : 9

2\(^x\)       = 16

2\(^x\)        = 2⁴

 \(x\)         = 4 

\(2^{x} .2+2^{x} =144\)

\(\Rightarrow 2^{x} .(2+1)=144\)

\(\Rightarrow 2^{x} .3=144\)

\(\Rightarrow 2^{x} =144:3\)

\(\Rightarrow 2^{x} =48\)

Mà không có số \(48\) nào được viết dưới dạng \(2^{x}\) nên \(x\in∅\)

Vậy \(x\in∅\)

\(2^x+2^{x+3}=144\)

\(\Rightarrow2^x\left(1+2^3\right)=144\)

\(\Rightarrow2^x.9=144\Rightarrow2^x=16\Rightarrow x=4\)

\(2^x+2^{x+3}=144\\ 2^x\left(1+2^3\right)=144\\ 2^x.9=144\\ 2^x=16\\ 2^x=2^4\\ \Rightarrow x=4\)

\(2^x+2^x+3=144\)

\(2\left(2^x\right)=144-3\)

\(2\left(2^x\right)=141\)

\(2^x=\frac{141}{2}\)

vô lí nhỉ????

\(x\)(\(x\) - 2) = 16

\(x^2\) - 2\(x\) - 16 = 0

(\(x^2\) - \(x\)) - (\(x\) - 1) - 17 = 0

\(x\)(\(x\) - 1) - (\(x-1\)) = 17

(\(x\) - 1)(\(x\) - 1) = 17

(\(x-1\))² = 17

\(\left[{}\begin{matrix}x-1=\sqrt{17}\\x-1=-\sqrt{17}\end{matrix}\right.\)

\(\left[{}\begin{matrix}x=1+\sqrt{17}\\x=1-\sqrt{17}\end{matrix}\right.\)

Vậy: \(\in\) {1 - \(\sqrt{17}\); 1 + \(\sqrt{17}\)}

Bài 2:

2^\(x\) + 3.2^\(x\) = 144

2^\(x\).(1 + 3) = 144

2^\(x\).4 = 144

2^\(x\) = 144 : 4

2^\(x\) = 36

2\(^x\) = 36

Nếu \(x\) = 6 ⇒ 2\(^x\) = 64 > 36 (loại)

Nếu \(x\) ≤ 5 ⇒2\(^x\) ≤ 2⁵ = 32 < 36 (loại)

Vậy \(x\in\) \(\varnothing\) 

2^x + 3 + 2^x = 144 
<=> 2^x (2^3 + 1) = 144 
<=> 2^x . 9 = 144 
<=> 2^x  = 16 
<=> x = 4

 2^x + 2^x+3 = 144

 2^x + 2^x . 2^3 = 144

 2^x ( 2^3 + 1 ) = 144

 2^x ( 8 + 1 ) = 144

 2^x . 9 = 144

 2^x = 144 : 9

 2^x = 16

 2^x = 2^4

=> x = 4