expand: $\ln (4a)^3$
- $3 \ln 4 + \ln a$
- $3 \ln 4 - 3 \ln a$
- $3 \ln 4 + 3 \ln a$

expand: $\ln \frac{2a^3}{b^4}$
- $\ln 2 + 3 \ln a - 4 \ln b$
- $\ln 2 - 3 \ln a - 4 \ln b$
- $\ln 2 - 3 \ln a + 4 \ln b$

Question

expand: $\ln (4a)^3$
- $3 \ln 4 + \ln a$
- $3 \ln 4 - 3 \ln a$
- $3 \ln 4 + 3 \ln a$

expand: $\ln \frac{2a^3}{b^4}$
- $\ln 2 + 3 \ln a - 4 \ln b$
- $\ln 2 - 3 \ln a - 4 \ln b$
- $\ln 2 - 3 \ln a + 4 \ln b$

Accepted Answer

{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Logarithmic Power Rule", "Logarithmic Product Rule", "Logarithmic Quotient Rule" ], "new_concepts": [], "current_concepts": [ "Logarithmic Power Rule", "Logarithmic Product Rule", "Logarithmic Quotient Rule" ] } ## Expand the first logarithmic expression Using the *Logarithmic Power Rule* and *Logarithmic Product Rule* knowledge points $$ \begin{aligned} \ln(4a)^3 &= 3\ln(4a) \ &= 3(\ln 4 + \ln a) \ &= 3\ln 4 + 3\ln a \end{aligned} $$ ## Expand the second logarithmic expression Using the *Logarithmic Quotient Rule*, *Logarithmic Product Rule*, and *Logarithmic Power Rule* knowledge points $$ \begin{aligned} \ln\frac{2a^3}{b^4} &= \ln(2a^3) - \ln(b^4) \ &= \ln 2 + \ln(a^3) - \ln(b^4) \ &= \ln 2 + 3\ln a - 4\ln b \end{aligned} $$ ## Question 1 (A) $3 \ln 4 + \ln a$

(B) $3 \ln 4 - 3 \ln a$

(C) $3 \ln 4 + 3 \ln a$ ## Question 2 (A) $\ln 2 + 3 \ln a - 4 \ln b$

(B) $\ln 2 - 3 \ln a - 4 \ln b$

(C) $\ln 2 - 3 \ln a + 4 \ln b$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Logarithmic Properties" ] }

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QUESTION IMAGE

Question

Explanation:

Expand the first logarithmic expression

Expand the second logarithmic expression

Answer:

Question 1

Question 2