1. **Problem statement:** Evaluate $\log_6 54 + \log_6 2 - \log_6 3$. 2. **Formula used:** The logarithm properties we use are: - $\log_b (xy) = \log_b x + \log_b y$ - $\log_b \left(\frac{x}{y}\right) = \log_b x - \log_b y$ 3. **Step-by-step solution:** Start with the expression: $$\log_6 54 + \log_6 2 - \log_6 3$$ Using the addition property of logarithms: $$= \log_6 (54 \times 2) - \log_6 3$$ Calculate inside the logarithm: $$= \log_6 108 - \log_6 3$$ Using the subtraction property: $$= \log_6 \left(\frac{108}{3}\right)$$ Simplify the fraction: $$= \log_6 36$$ 4. **Final evaluation:** Since $36 = 6^2$, we have: $$\log_6 36 = \log_6 (6^2) = 2$$ **Answer:** $2$