Question

3log(x^2.y) = 4+2logx-logy and x-y=2√8. Find x and y.

Answer 1

We have
3log(x^2.y) = 4+2logx-logy
by property of logarithmic equations we can rewrite above equation
3{2log(x) + log(y)} = 4+2logx-logy
6logx-3logy = 4+2logx-logy
4logx+4logy = 4
log(xy) = 1
taking antilog both side
xy = 10.
now we have given that x-y=2√8
from above equation y = 10/x. putting this in given equation x-y=2√8 we get
x - 10/x = 2√8
x^2 - 2√8x - 10 = 0
solving above equation we get 
x = 5√2 or -√2
now y = 10/x
then y = √2 or -5√2.