1. **State the problem:** Expand the logarithmic expression $$\log(xz^3)$$ using the properties of logarithms. 2. **Recall the properties of logarithms:** - The logarithm of a product is the sum of the logarithms: $$\log(ab) = \log a + \log b$$ - The logarithm of a power is the exponent times the logarithm: $$\log(a^n) = n \log a$$ 3. **Apply the product rule:** $$\log(xz^3) = \log x + \log z^3$$ 4. **Apply the power rule:** $$\log x + \log z^3 = \log x + 3 \log z$$ 5. **Final expanded form:** $$\log(xz^3) = \log x + 3 \log z$$ This expression now has each logarithm involving only one variable and no exponents inside the logarithm.