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