यदि `(2^(x))(2^(y))=8` और `(9^(x))(3^(y))=81` है तो `(x,y)=?`

Options

A. `(1,2)`
B. `(2,1)`
C. `(1,1)`
D. `(2,2)`

Answer

A

Explanation

`2^(x).2^(y)=8implies2^(x+y)=2^(3)`
`x+y=3`…………i
`9^(x).3^(y)=81`
`3^(2x).3^(y)=3^(4)`
`implies 2xy=4`……………ii
From equation i and ii

`x=1`
`x=2`
`:. (x,y)=(1,2)`