1. The problem asks to write the expression $\log(8x^3) + \log(2x)$ as a single logarithm. 2. Recall the logarithm property: $\log(a) + \log(b) = \log(ab)$. 3. Apply this property to combine the logs: $$\log(8x^3) + \log(2x) = \log\left(8x^3 \cdot 2x\right)$$ 4. Multiply inside the logarithm: $$8x^3 \cdot 2x = 16x^4$$ 5. So the expression becomes: $$\log(16x^4)$$ 6. The options given are: - $4 \log(x)$ - $4 \log(2x)$ - $\log(8x^3 + 2x)$ - $4 \log(x^4)$ - $\log(10x^4)$ 7. None of these exactly matches $\log(16x^4)$ but the correct single logarithm form is $\log(16x^4)$. 8. Since none of the given choices match, the correct expression is:\n $$\log(16x^4)$$ Slug: "logarithm sum" Subject: "algebra" Desmos: {"latex":"y=\log(16x^4)","features":{"intercepts":true,"extrema":true}} q_count: 1