SOLUTION: how do i solve this system of equations {{{ ln x = 3ln y}}} {{{ 3^x = 27^y }}}

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Question 91693: how do i solve this system of equations
+ln+x+=+3ln+y
+3%5Ex+=+27%5Ey+
Answer by psbhowmick(878) About Me  (Show Source):
You can put this solution on YOUR website!
ln%28x%29+=+3ln%28y%29
ln%28x%29+=+ln%28y%5E3%29
ln%28x%29+-+ln%28y%5E3%29+=+0
ln%28x%2Fy%5E3%29+=+0
x%2Fy%5E3+=+1
x+=+y%5E3 __________ (1)

3%5Ex+=+27%5Ey
3%5Ex+=+%283%5E3%29%5Ey
3%5Ex+=+3%5E%283y%29
x+=+3y ___________ (2)

Substituting x from (1) in (2)
y%5E3+=+3y
y%5E3+-+3y+=+0
y%28y%5E2+-+3%29+=+0
y%28y+%2B+sqrt%283%29%29%28y+-+sqrt%283%29%29+=+0
Either y+=+0, y+=+-+sqrt%283%29 or y+=+sqrt%283%29
Accordingly, x+=+0, x+=+-+3sqrt%283%29 or x+=+3sqrt%283%29

But since logarithm of negative numbers is undefined so x+=+-3sqrt%283%29,y+=+-sqrt%283%29 is not a solution.

Hence, the solutions are x+=+0,+y+=+0and x+=+3sqrt%283%29,y+=+sqrt%283%29.