recall that log_a(b) = ln(a)/ln(b)
So, converting everything to natural logs (or any set of logs with a common base),
ln3/ln25 x + ln7/ln2 y = ln27/ln5
ln8/ln7 x + ln5/ln3 y = ln2/ln49
Now just solve the system as usual. It's messy, but it's just numbers. If you don't need an exact solution, just convert everything to decimal coefficients.
How do you solve a system of logarithmic equations? They have completely different bases:
{(log(25)^3)x + (log(2)^7)y = log(5)^27
{(log(7)^8)x + (log(3)^5)y = log(49)^2
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