Question

Tìm \(x\in Q\), biết:

\(2^{x+3}+2^{x+1}=320\)

Answer 1

2^x+3+2^x+1=320

2^x.2³+2^x.2=320

2^x.(2³+2)=320

2^x.10=320

2^x=32=2⁵

       Vậy x=5

 

Answer 2

Ta có: \(2^{x+3}+2^{x+1}=2^{x+1}.2^2+2^{x+1}=2^{x+1}\left(4+1\right)=2^{x+1}.5=320\)

\(\Rightarrow2^{x+1}=\frac{320}{5}=64\)

\(\Rightarrow2^{x+1}=2^6\Rightarrow x+1=6\Rightarrow x=5\)