1. **State the problem:** We need to verify if the expression $$\log_2 \left( \frac{x}{3} + 5 \right) - \log_2 (16)$$ is correctly simplified to $$\log_2 \left( \frac{x}{48} + \frac{5}{16} \right).$$ 2. **Recall the logarithm subtraction rule:** For any positive numbers $a$ and $b$, and base $c > 0$, $c \neq 1$, we have $$\log_c(a) - \log_c(b) = \log_c \left( \frac{a}{b} \right).$$ 3. **Apply the rule:** $$\log_2 \left( \frac{x}{3} + 5 \right) - \log_2 (16) = \log_2 \left( \frac{\frac{x}{3} + 5}{16} \right).$$ 4. **Simplify the fraction inside the logarithm:** $$\frac{\frac{x}{3} + 5}{16} = \frac{x}{3 \times 16} + \frac{5}{16} = \frac{x}{48} + \frac{5}{16}.$$ 5. **Conclusion:** The simplification is correct because $$\log_2 \left( \frac{x}{3} + 5 \right) - \log_2 (16) = \log_2 \left( \frac{x}{48} + \frac{5}{16} \right).$$