Answer: \(rs=6561\).

We start with the main method. Rewrite all logarithms using a common base, then combine them using the product and power laws.

Use change of base for \(\log_9s\):

\(\log_9s=\frac{\log_3s}{\log_39}=\frac{\log_3s}{2}.\)

Therefore

\(2\log_9s=\log_3s.\)

The equation becomes

\(\log_3r+\log_3s=8.\)

Using the logarithm law,

\(\log_3(rs)=8.\)

Hence

\(rs=3^8=6561.\)

This completes the solution and gives the required result.