Question

Tìm x

2^x + 2^x+1 + 2^x+2 + 2^x+3=480

Answer 1

`2^x + 2^(x+1) + 2^(x+2) + 2^(x+3) = 480`

`=> 2^x + 2^x . 2 + 2^x . 4 + 2^x . 8 = 480`

`=> 2^x . (1 + 2 + 4 + 8) = 480`

`=> 2^x . 15 = 480`

`=> 2^x = 32`

`=>2^x = 2^5`

`=> x = 5`

Vậy `x = 5`

Answer 2

`2^x + 2^{x+1} + 2^{x+2} + 2^{x+3} =480`

`=> 2^x * 1 + 2^x * 2 + 2^x * 4 + 2^x * 8 = 480`

`=> 2^x*(1 + 2 + 4 + 8) = 480`

`=> 2^x* 15 = 480`

`=> 2^x = 480 : 15`

`=> 2^x = 32`

`=> 2^x = 2^5`

`=> x = 5`

Vậy `x = 5`

Answer 3

\(2^x+2^{x+1}+2^{x+2}+2^{x+3}=480\)
\(2^x+2^x.2+2^x.2^2+2^x.2^3=480\)
\(2^x.\left(1+2+2^2+2^3\right)=480\)
\(2^x\left(1+2+4+8\right)=480\)
\(2^x.15=480\)
\(2^x=480:15\)
\(2^x=32\)
\(2^x=2^5\)
\(x=5\)
Vậy...