Question

[nga]

Gía trị của \(x+y\) biết \(2^x=8^{y+1}\) và \(9^y=3^{x-9}\left(x,y\in N\right)\)

Answer 1

[Võ Đông Anh Tuấn]

\(2^x=2^{3\left(y+1\right)}\Rightarrow x=3y+3\)

\(3^{2y}\Rightarrow3^{x-9}\Rightarrow2y=x-9\Rightarrow x=2y+9\)

\(\Rightarrow3y+3=2y+9\Rightarrow y=6\Rightarrow x=21\Rightarrow x+y=27\)

Answer 2

[Phạm Nguyễn Tất Đạt]

Ta có:\(2^x=8^{y+1}\Rightarrow2^x=2^{3\left(y+1\right)}\Rightarrow2^x=2^{3y+3}\Rightarrow x=3y+3\)

\(\Rightarrow9^y=3^{x-9}\Rightarrow3^{2y}=3^{3y+3-9}\Rightarrow3^{2y}=3^{3y-6}\Rightarrow2y=3y-6\)

\(\Rightarrow2y-3y=-6\Rightarrow-y=-6\Rightarrow y=6\)

\(\Rightarrow x=6\cdot3+3=21\)

\(\Rightarrow x+y=21+6=27\)