If \[\log{x} = 2 + \log{y} = \log{\frac{4}{9}} - \log{\frac{9}{125}} + 2\log{\frac{9}{5}},\] where all logarithms are to base \(10\), find \(x\) and \(y\) without using tables.

Which rules do you know to simplify expressions with logarithms? Can you use them to simplify the above equation?