1. **State the problem:** Express $\log_9 x$ in terms of $\log_3 x$ and $\log_3 y$. 2. **Recall the change of base formula:** For any positive numbers $a,b,c$ with $a \neq 1$, $$\log_a b = \frac{\log_c b}{\log_c a}$$ This allows us to rewrite logarithms in terms of a different base. 3. **Apply the formula to $\log_9 x$ using base 3:** $$\log_9 x = \frac{\log_3 x}{\log_3 9}$$ 4. **Simplify $\log_3 9$:** Since $9 = 3^2$, $$\log_3 9 = \log_3 3^2 = 2 \log_3 3 = 2 \times 1 = 2$$ 5. **Substitute back:** $$\log_9 x = \frac{\log_3 x}{2}$$ 6. **Express $\log_3 x$ in terms of $\log_3 y$ if needed:** If you want to express $\log_3 x$ using $\log_3 y$, you can write $$\log_3 x = \log_3 y \times \frac{\log_3 x}{\log_3 y}$$ but without additional relations between $x$ and $y$, this is the simplest form. **Final answer:** $$\boxed{\log_9 x = \frac{\log_3 x}{2}}$$