expand each expression.

$\ln (2x)^4$
- $4 \ln 2 + 4 \ln x$
- $4 \ln 2 + \ln x$
- $8 \ln x$

$\ln \frac{4y^5}{x^2}$
- $\ln 4 - 2 \ln x - 5 \ln y$
- $\ln 4 - 2 \ln x + 5 \ln y$
- $-8 \ln x + 5 \ln y$

Question

expand each expression.

$\ln (2x)^4$
- $4 \ln 2 + 4 \ln x$
- $4 \ln 2 + \ln x$
- $8 \ln x$

$\ln \frac{4y^5}{x^2}$
- $\ln 4 - 2 \ln x - 5 \ln y$
- $\ln 4 - 2 \ln x + 5 \ln y$
- $-8 \ln x + 5 \ln y$

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 expression Using the *Logarithmic Power Rule* and *Logarithmic Product Rule* knowledge points $$ \begin{aligned} \ln(2x)^4 &= 4\ln(2x) \ &= 4(\ln 2 + \ln x) \ &= 4\ln 2 + 4\ln x \end{aligned} $$ ## Expand the second expression Using the *Logarithmic Quotient Rule*, *Logarithmic Product Rule*, and *Logarithmic Power Rule* knowledge points $$ \begin{aligned} \ln\frac{4y^5}{x^2} &= \ln(4y^5) - \ln(x^2) \ &= \ln 4 + \ln(y^5) - \ln(x^2) \ &= \ln 4 + 5\ln y - 2\ln x \ &= \ln 4 - 2\ln x + 5\ln y \end{aligned} $$ ## Question 1 (A) $4 \ln 2 + 4 \ln x$

(B) $4 \ln 2 + \ln x$

(C) $8 \ln x$ ## Question 2 (A) $\ln 4 - 2 \ln x - 5 \ln y$

(B) $\ln 4 - 2 \ln x + 5 \ln y$

(C) $-8 \ln x + 5 \ln y$

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

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QUESTION IMAGE

Question

Explanation:

Expand the first expression

Expand the second expression

Answer:

Question 1

Question 2