Question

Tìm x biết:2^x+2^x+1+2^x+2+2^x+3=120

 

Answer 1

2^x + 2^x+1 +2^x+2 + 2^x+3 = 120

Suy ra 2^x .1 + 2^x . 2 + 2^x . 2² + 2^x . 2³ = 120

Suy ra 2^x .( 1 + 2 + 4 + 8 ) = 120

Suy ra 2^x . 15 = 120

Suy ra 2^x = 120 : 15

Suy ra 2^x = 8

Suy ra 2^x = 2³

Do đó x = 3

Vậy x = 3

Answer 2

\(2^x+2^{x+1}+2^{x+2}+2^{x+3}=120\)

\(\Rightarrow2^x+2^x.2+2^x.2^2+2^x.2^3=120\)

\(\Rightarrow2^x+2^x.2+2^x.4+2^x.8=120\)

\(\Rightarrow2^x\left(1+2+4+8\right)=120\)

\(\Rightarrow2^x.15=120\)

\(\Rightarrow2^x=120:15\)

\(\Rightarrow2^x=8\)

\(\Rightarrow2^x=2^3\)

\(\Rightarrow x=3\)