Question

\(\text{3x2^x+2^x+1+2^xx2^2=576}\)

Answer 1

\(3\cdot2^x+2^{x+1}+2^x\cdot2^2=576\)

\(\Rightarrow3\cdot2^x+2^x\cdot2+2^x\cdot4=546\)

\(\Rightarrow\left(3+2+4\right)\cdot2^x=576\)

\(\Rightarrow9\cdot2^x=576\)

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

\(\Rightarrow2^x=64\)

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

\(\Rightarrow x=6\)

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