Question

2^{3 + x} + 2^x = 576. 

 

Answer 1

\(2^{3+x}+2^x=576\)

\(\Rightarrow2^x\cdot2^3+2^x=576\)

\(\Rightarrow2^x\cdot\left(2^3+1\right)=576\)

\(\Rightarrow2^x\cdot\left(8+1\right)=576\)

\(\Rightarrow2^x\cdot9=576\)

\(\Rightarrow2^x=576:9\)

\(\Rightarrow2^x=64\)

\(\Rightarrow2^x=2^6\)

\(\Rightarrow x=6\)

Vậy $x=6$.

Answer 2

\(2^{3+x}+2^x=576.\)

\(2^3.2^x+2^x.1=576\)

\(2^x.\left(2^3+1\right)=576\)

\(2^x.9=576\)

\(2^x=576:9\)

\(2^x=64\)

\(2^x=2^6\)

\(\Rightarrow x=6\)