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

10 years ago

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

10 years ago

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.