2logxbase5+3logybase3=8
and
6logxbase5+2logybase3=2
solve silmultaneously
just for ease of readability, let's say
u = log5x
v = log3y
Then we have
2u+3v=8
6u+2v=2
This has the solution
u = -5/7
v = 22/7
Unusual for a problem of this kind, but anyway...
log5x = -5/7, so x = 5^(-5/7)
log3y = 22/7, so y = 3^(22/7)