2^x + 2^x +4 = 272

(2 + 2)^x  + 4 = 272

   4^x      + 4 = 272

        4^x       = 272 - 4

        4^x       = 268

2^x+2^x.2⁴=272

2^x(2⁴+1)=272

2^x.17=272

2^x=16

x=4

7,0660819

\(2^x+2^{x+4}=272\)

\(2^x+2^{x+4}=272\)

\(\Rightarrow2^x+2^x\cdot2^4=272\)

\(\Rightarrow2^x\left(1+2^4\right)=272\)

\(\Rightarrow2^x\cdot17=272\)

\(\Rightarrow2^x=272:17=16\)

\(\Rightarrow2^x=2^4\Rightarrow x=4\)

\(1,\sqrt{3}x-3=\sqrt{27}\)

\(\Leftrightarrow\sqrt{3}x-3=3\sqrt{3}\)

\(\Leftrightarrow\sqrt{3}\left(x-\sqrt{3}\right)=3\sqrt{3}\)

\(\Leftrightarrow x-\sqrt{3}=3\)

\(\Leftrightarrow x=3+\sqrt{3}\)

\(2,\sqrt{2}x-\sqrt{28}=\sqrt{32}\)

\(\Leftrightarrow\sqrt{2}x-2\sqrt{7}=4\sqrt{2}\)

\(\Leftrightarrow\sqrt{2}x=4\sqrt{2}+2\sqrt{7}\)

\(\Leftrightarrow x=\dfrac{\sqrt{2^2}\left(2\sqrt{2}+\sqrt{7}\right)}{\sqrt{2}}\)

\(\Leftrightarrow x=\sqrt{2}\left(2\sqrt{2}+\sqrt{7}\right)\)

\(\Leftrightarrow x=4+\sqrt{14}\)

\(3,\sqrt{6}x-2\sqrt{6}=\sqrt{54}\)

\(\Leftrightarrow\sqrt{6}\left(x-2\right)=3\sqrt{6}\)

\(\Leftrightarrow x-2=3\)

\(\Leftrightarrow x=5\)

\(4,\sqrt{3}x-\sqrt{2}x=\sqrt{3}+\sqrt{2}\)

\(\Leftrightarrow\left(\sqrt{3}-\sqrt{2}\right)x=\sqrt{3}+\sqrt{2}\)

\(\Leftrightarrow x=\dfrac{\sqrt{3}+\sqrt{2}}{\sqrt{3}-\sqrt{2}}\)

2^x + 2^x+4 = 272

=> 2^x(1 + 2⁴ ) = 272

=> 2^x . 17 = 272

=> 2^x = 272 : 17 = 16

=> 2^x  = 2⁴

=> x = 4

2^x.17 = 272

2^x = 2⁴

x = 4           

=>2^x+2^x.2⁴=272

=>2^x.(1+2⁴)=272

=>2^x.17=272

=>2^x=16

=>2^x=2⁴

=>x=4

Vậy x=4

L-i-k-e cho mình nha mình đang rất cần điểm

a) \(5.3^x=405\)

\(\Rightarrow3^x=405:5\)

\(\Rightarrow3^x=81=3^4\)

\(\Rightarrow x=4\)

b) \(\left(x-2\right)^5=243\)

\(\Rightarrow\left(x-2\right)^5=3^5\)

\(\Rightarrow x-2=3\)

\(\Rightarrow x=5\)

c) \(2^x+2^{x+4}=272\)

\(\Rightarrow2^x.\left(1+2^4\right)=272\)

\(\Rightarrow2^x.17=272\)

\(\Rightarrow2^x=272:17=16\)

\(\Rightarrow2^x=2^4\)

\(\Rightarrow x=4\)

d) Từ x + 1 đến x + 2 có số số hạng là: (30 - 1) : 1 + 1 = 30 (số)

\(\left(x+1\right)+\left(x+2\right)+...+\left(x+30\right)=795\)

\(\Rightarrow30x+\frac{\left(30+1\right).30}{2}=795\)

\(\Rightarrow30x+465=795\)

\(\Rightarrow30x=330\)

\(\Rightarrow x=330:30\)

\(\Rightarrow x=11\)

a) \(5.3^x=405\)

         \(3^x=\frac{405}{5}=81\)

          \(3^x=3^4\)

Vậy x = 4

b ) \(\left(x-2\right)^5=243\)

      \(\left(x-2\right)^5=3^5\)

\(\Rightarrow x-2=3\)

\(\Rightarrow x=3+2=5\)

     Vậy x = 5

a, 5.3 ^x =405

3^x=405:5

3^x=81

=> x=4

b, (x-2)⁵=243

(x-2)⁵=3⁵

vì 5=5

nên x -2=3

<=> x=3+2

=>x=5

c, 2x  +   2x+4  =  272 

2^x+2^x+2⁴=272

2^x(1+2⁴)=272

2^x.17=272

2^x=272:17

2^x=16

vì 16=2⁴

=>x=4

d, (x+1)+(x+2)+(x+3)+.....+(x+30)=795

(x+x+x+..+x)+(1+2+3+..+30)=795

30x+456=795

30x=795-456

30x=330

x=330:30

x=11

vậy x=11

hc tốt

2^x + 2^{x + 4} = 272

=> 2^x + 2^x . 2⁴ = 272

=> 2^x .( 1 + 2⁴ ) = 272

=> 2^x . 17 = 272

=> 2^x = 272 : 17 = 16

=> 2^x = 2⁴

=> x = 4

Vậy x = 4

tách số thứ 2 thành 2 ^ x . 2^ 4 có chung nhe làm bình thường nha

\(2^x+2^{x+4}=272\)

\(2^x+2^x\cdot2^4=272\)

\(2^x\left(1+16\right)=272\)

\(2^x\cdot17=272\)

\(2^x=272:17\)

\(2^x=16\)

\(\Rightarrow x=4\)

2^x+2^x+4=272

=> 2^x.(1+2⁴)=272

=> 2^x.(1+16)=272

=> 2^x.17=272

=> 2^x=272:17

=> 2^x=16

=> 2^x=2⁴

=> x=4