The number of solution pairs (x , y) of the simultaneous equations `log_(1//3) (x + y) + "log"_(3) (x-y) = 2` and `2^(y^(2)) = 512^(x + 1)` is

Options

A. 0
B. 1
C. 2
D. 3

Answer

B

Explanation

`"log"_(3^(-1)) (x + y) + "log"_(3)( x - y) = 2`
`-"log"_(3) (x +y) + "log"_(3) (x - y) = 2`
`"log"_(3) ((x - y)/(x + y)) = 2 `
`( x - y)/(x + y) = 9`
`2^(y^(2)) = (2^(9))^(x + 1)`
`2^(y^(2)) = 2^(9^(x + 1))`
`y^(2) = 9(x + 1)`
Solve eliminate y
`16x^(2) - 225 x -225 = 0 `
x = 15 , `(-15)/(16)`
At x = 15 , y = `-12`
x = `(-15)/(16) , y = (3)/(4)` ( not possible )
only sol . x = 15, y = `-12` only one sol.