1. The problem asks why the expression $\frac{x+15}{3}$ was rewritten as $\frac{x}{3} + 5$ in Example 1. 2. Recall the property of division over addition: $$\frac{a+b}{c} = \frac{a}{c} + \frac{b}{c}$$ 3. Applying this to $\frac{x+15}{3}$, we get: $$\frac{x+15}{3} = \frac{x}{3} + \frac{15}{3}$$ 4. Simplify $\frac{15}{3}$: $$\frac{15}{3} = 5$$ 5. Therefore: $$\frac{x+15}{3} = \frac{x}{3} + 5$$ 6. This step is important because it separates the terms to make the logarithmic expression easier to handle and understand. Final answer: $\frac{x+15}{3} = \frac{x}{3} + 5$