Question

Tìm số nguyên x, y:

a) 3^{x + 2} . 5^{y - 3} = 45^x

b) 8^x + 80 = 3^{y + 2}

c) -3 . 3^x + 3^x . 5 = 162

d) 5 . 2^-2 . 2^{x + 1} - 2^x = 384

e) 7 . 4^{x - 2} - 4^x = -38

Answer 1

a) \(3^{x+2}\cdot5^{y-3}=45^x\)

\(\Rightarrow3^{x+2}\cdot5^{y-3}=\left(3^2\right)^x\cdot5^x\)

\(\Rightarrow3^{x+2}\cdot5^{y-3}=3^{2x}\cdot5^x\)

\(\Rightarrow\left\{{}\begin{matrix}3^{x+2}=3^{2x}\\5^{y-3}=5^x\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}x+2=2x\\y-3=x\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}x=2\\y-3=2\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}x=2\\y=5\end{matrix}\right.\)