1. **State the problem:** Solve the equation $$\frac{\log_3 9 - 22}{\log_3 9 - 5} = 4$$. 2. **Recall the properties of logarithms:** - $\log_b a^n = n \log_b a$ - $\log_b b = 1$ 3. **Simplify the logarithms:** Since $9 = 3^2$, we have: $$\log_3 9 = \log_3 (3^2) = 2$$ 4. **Substitute the values into the equation:** $$\frac{2 - 22}{2 - 5} = 4$$ 5. **Simplify numerator and denominator:** $$\frac{-20}{-3} = 4$$ 6. **Simplify the fraction:** $$\frac{\cancel{-20}}{\cancel{-3}} = \frac{20}{3}$$ 7. **Check if the fraction equals 4:** $$\frac{20}{3} \neq 4$$ 8. **Conclusion:** The equation as given is not true with the values substituted, so there might be a misunderstanding or typo in the problem statement. **Final answer:** The left side simplifies to $\frac{20}{3}$, which does not equal 4, so the equation is false as stated.