Question

Tìm x,y

a, 2^x+1 x 3^y = 12^x

b, 10^x : 5^y = 20^y

Answer 1

b. \(10^x:5^y=20^y\)

\(\Leftrightarrow10^x=20^y.5^y=100^y\)

\(\Leftrightarrow10^x=\left(10^2\right)^y\)

\(\Leftrightarrow x=2y\)

Answer 2

a, 2^x+1 . 3^y = 12^x

=> \(3^y=\dfrac{12^x}{2^{x+1}}\)

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

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

=> 3^y=3^x

=> x=y

Answer 3

a. Ta có: \(2^{x+1}.3^y=12^x\)

\(\Leftrightarrow2^{x+1}.3^y=\left(2^2.3\right)^x\)

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

\(\Leftrightarrow\left\{{}\begin{matrix}2^{x+1}=2^{2x}\\3^y=3^x\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x+1=2x\\y=x\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=1\\y=x\end{matrix}\right.\)

Vậy x = y = 1

Answer 4

b.