1. **Problem statement:** Expand the logarithmic expressions using the properties of logarithms. 2. **Recall the properties:** - $\log_a(xy) = \log_a x + \log_a y$ - $\log_a\left(\frac{x}{y}\right) = \log_a x - \log_a y$ - $\log_a(x)^r = r \log_a x$ - $\log_a 1 = 0$ - $\log_a a = 1$ 3. **Example 1: Expand $\log_7(5x)$** - Using the product property: $\log_7(5x) = \log_7 5 + \log_7 x$ 4. **Example 2: Expand $\log_4 x^3$** - Using the power property: $\log_4 x^3 = 3 \log_4 x$ **Final answers:** - $\log_7(5x) = \log_7 5 + \log_7 x$ - $\log_4 x^3 = 3 \log_4 x$