identify the solution set of $3 \ln 4 = 2 \ln x$.

* $\{6\}$
* $\{-8, 8\}$
* $\{8\}$

Question

identify the solution set of $3 \ln 4 = 2 \ln x$.

* $\{6\}$
* $\{-8, 8\}$
* $\{8\}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Logarithmic Power Rule", "Solving Logarithmic Equations" ], "new_concepts": [], "current_concepts": [ "Logarithmic Power Rule", "Solving Logarithmic Equations" ] } ## Apply the logarithmic power rule Using the *Logarithmic Power Rule* knowledge point $$ \begin{aligned} &3 \ln 4 = \ln(4^3) = \ln 64 \ &2 \ln x = \ln(x^2) \quad (x > 0) \end{aligned} $$ ## Equate the arguments and solve for x Using the *Solving Logarithmic Equations* knowledge point $$ \begin{aligned} &\ln 64 = \ln(x^2) \ &x^2 = 64 \ &x = \pm 8 \end{aligned} $$ ## Check the domain restriction Using the *Solving Logarithmic Equations* knowledge point $$ \begin{aligned} &\text{Since } \ln x \text{ requires } x > 0, \ &x = 8 \text{ is the only valid solution.} \end{aligned} $$

{6}

{-8, 8}

{8}

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

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QUESTION IMAGE

Question

Explanation:

Apply the logarithmic power rule

Equate the arguments and solve for x

Check the domain restriction

Answer: