1. **State the problem:** Simplify the expression $$\log(12x^4) - \log(4x)$$ into a single logarithm. 2. **Recall the logarithm property:** The difference of logarithms with the same base can be written as the logarithm of a quotient: $$\log(a) - \log(b) = \log\left(\frac{a}{b}\right)$$ 3. **Apply the property:** $$\log(12x^4) - \log(4x) = \log\left(\frac{12x^4}{4x}\right)$$ 4. **Simplify the fraction inside the logarithm:** $$\frac{12x^4}{4x} = \frac{\cancel{12}^3 x^{4}}{\cancel{4}^1 x^{1}} = 3x^{4-1} = 3x^3$$ 5. **Write the final simplified expression:** $$\log(3x^3)$$ **Answer:** $$\log(3x^3)$$