Theo đề, ta có: \(\left\{{}\begin{matrix}2^{2x}=2^{3x+3y}\\3^{2x+2y}=3^{5+5y}\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x+3y=0\\2x-3y=5\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{5}{3}\\y=-\dfrac{5}{9}\end{matrix}\right.\)

Ta có: \(\frac{4^x}{2^{x+y}}=8=>2^{2x}=2^3.2^{x+y}=>2^{2x}=2^{3+x+y}\)

\(=>2x=3+x+y=>x=3+y\)(1)

\(\frac{9^{x+y}}{3^{5y}}=243=>3^{3\left(x+y\right)}=3^5.3^{5y}\)

\(=>3^{3x+3y}=3^{5+5y}\)

=>3x + 3y = 5 + 5y

3x - 5 = 2y (2)

Thay (1) vào (2), có:

3.(3+y) - 5 = 2y

9 + 3y - 5= 2y

y = -4

=> x= 3 + -4 = -1

Vậy xy = -1 . (-4) = 4

cx có tình trạng tự ra câu hỏi rồi tự làm nx hả

Làm để đó, ai ko bik làm thì hok xem, vs lại có ng hỏi bài này, viết lên như thế dễ hiểu

x.y=4 chắc chắn đúng

\(\frac{4^x}{2^{x+y}}=8\)

\(\frac{2^{2x}}{2^x.2^y}=8\)

\(\frac{2^x}{2^y}=8\)

\(2^x=2^3.2^y\)

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

\(\Rightarrow x=3+y\)

\(\frac{9^{x+y}}{3^{5y}}=243\)

\(\frac{3^{2x+2y}}{3^{5y}}=3^5\)

\(\frac{3^{2x}.3^{2y}}{3^{5y}}=3^5\)

\(\frac{3^{2x}}{3^{3y}}=3^5\)

\(3^{2x}=3^5.3^{3y}\)

\(3^{2x}=3^{5+3y}\)

\(\Rightarrow2x=3y+5\)

\(\hept{\begin{cases}2x-3y=5\\x=3+y\end{cases}}\Leftrightarrow\hept{\begin{cases}2\left(3+y\right)-3y=5\\x=3+y\end{cases}}\)

\(\Leftrightarrow\hept{\begin{cases}6+2y-3y=5\\x=3+y\end{cases}}\Leftrightarrow\hept{\begin{cases}-y=-1\\x=3+y\end{cases}}\)

\(\Leftrightarrow\hept{\begin{cases}y=1\\x=4\end{cases}}\)

vậy...

\(\frac{4^x}{2^{x+y}}=8\Leftrightarrow2^{2x}=2^{x+y+3}\Leftrightarrow x=y+3\)

\(9^{x+y}=243.3^{5y}\Leftrightarrow3^{2x+2y}=3^{5y+5}\Leftrightarrow2x=3y+5\)

\(\left(x,y\right)=\left(-1;2\right)\)

\(\frac{4^x}{2^{x+y}}=8\)

\(\frac{2^{2x}}{2^{x+y}}=2^3\)

\(2x-\left(x+y\right)=3\)

\(x-y=3\)

\(2x-2y=6\)

\(\frac{9^{x+y}}{3^{5y}}=243\)

\(\frac{3^{2x+2y}}{3^{5y}}=3^5\)

\(2x+2y-5y=5\)

\(2x-3y=5\)

mà \(2x-2y=6\)

\(\left(2x-3y\right)-\left(2x-2y\right)=5-6\)

\(-y=-1\)

y = 1

x = 4

Vậy xy = 4

Bài 1:

Bài 2:

\(\frac{4^x}{2^{x+y}}=8\Leftrightarrow4^x=8.2^{x+y}\Leftrightarrow\left(2^2\right)^x=2^3.2^{x+y}\Leftrightarrow2^{2x}=2^{x+y+3}\)<=>2x=x+y+3<=>x=y+3

\(\frac{9^{x+y}}{3^{5y}}=243\Leftrightarrow9^{x+y}=243.3^{5y}\Leftrightarrow\left(3^2\right)^{x+y}=3^5.3^{5y}\Leftrightarrow3^{2x+2y}=3^{5y+5}\)<=>2x+2y=5y+5

<=>2x=3y+5 mà x=y+3 => 2(y+3)=3y+5 <=> 2y+6=3y+5 <=> 6-5=3y-2y <=> y=1 <=> x=1+3=4

Vậy xy=4.1=4

\(\frac{9^{x+y}}{3^{5y}}=243\Leftrightarrow\frac{9^{x+y}}{3^{5y}}=\frac{9^{4+1}}{3^{5\cdot1}}\Leftrightarrow x=4,y=1..\)

vậy x=4.y=1

Ai giúp mk đi làm ơn đó mai mk phải nộp rùi T_T

\(\frac{4^x}{2^{x+y}}=8\Leftrightarrow\frac{4^x}{2^{x+y}}=\frac{4^4}{2^{4+1}}\Rightarrow x=4,y=1.\)

vậy x=4 y=1