Question

2^x+1.3^y=12^x

Answer 1

\(\Leftrightarrow2^{x+1}.3^y=2^{2x}.3^x\)

\(\Leftrightarrow\dfrac{2^{2x}.3^x}{2^{x+1}.3^y}=1\Leftrightarrow2^{x-1}.3^{x-y}=1\)

\(\Leftrightarrow\dfrac{2^x3^{x-y}}{2}=1\Leftrightarrow2^x.3^{x-y}=2\)

\(\Leftrightarrow2^x.3^{x-y}=2^1.3^0\)

\(\Leftrightarrow\left\{{}\begin{matrix}x=1\\x-y=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=1\\y=1\end{matrix}\right.\)

Answer 2

Ta có 2^{x + 1} . 3^y = 12^x

2^{x + 1} . 3^y = 2^2x . 3^x

⇒ x + 1 = 2x

    x = y 

Vậy x = y = 1