Question

2^x+1.3^y=12^x

 

Answer 1

<=> 2^x+1 * 3^y = 2^2x * 3^x

=> \(\hept{\begin{cases}x+1=2x\\x=y\end{cases}}\Rightarrow\hept{\begin{cases}x=1\\y=1\end{cases}}\)

Answer 2

2^x+1.3^y=12^x

2^x+1.3^y=4^x.3^x

2^x+1.3^y=(2²)^x.3^x

2^x+1.3^y=2^2x.3^x

=> 3^y:3^x=2^2x:2^x+1

=> 3^y-x=2^x-1

Mà (2,3)=1 => 3^y-x=2^x-1=1

=> y-x=0; x-1=0

=> x=y=1

Vậy x=y=1