Log2 y = log4(xy-2), log9 x2 +log3 (x-y) = 1Find x & y

Dear student,

It is

logy=1/2log(xy-2)

y=(xy-2)^1/2

y2=xy-2

Similaryly get an equation from the 2nd one...

solve the two to find x and y

Log₂Y=log₄(xy-2)

log₂Y=log₂²(xy-2)

log₂y=(1/2)*log₂(xy-2)

2log₂y=log₂(xy-2)

log₂y²= log₂(xy-2)

log₂y² - log₂(xy-2) = 0

log₂y² - log₂(xy-2) = log₂1

log₂(y²/xy-2)= log₂1

y²/xy-2 = 1

y² = xy-2 ......(1).

Similarly for log₉x² + log₃(x-y) = 1

 log₃²x² + log₃(x-y) = log₃3.

2/2log₃x + log₃(x-y) = log₃3

log₃x+log₃(x-y) = log₃3

log₃(x*(x-y))= log₃3

x(x-y) = 1 ..............(2).

Now solve equations (1)&(2) and you will get the answer. 

if you are satisfied with the solution than approve.