identify the solution set of $3 \ln 4 = 2 \ln x$.
- $\{6\}$
- $\{-8, 8\}$
- $\{8\}$

identify the solution set of $6 \ln e = e^{\ln 2x}$.
- $\{2\}$
- $\{3\}$
- $\{6\}$

Question

identify the solution set of $3 \ln 4 = 2 \ln x$.
- $\{6\}$
- $\{-8, 8\}$
- $\{8\}$

identify the solution set of $6 \ln e = e^{\ln 2x}$.
- $\{2\}$
- $\{3\}$
- $\{6\}$

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": [ "Solving Logarithmic Equations", "Logarithmic Power Rule" ], "new_concepts": [], "current_concepts": [ "Solving Logarithmic Equations", "Logarithmic Power Rule", "Inverse Properties of Logarithms" ] } ## Solve the first logarithmic equation Using the *Logarithmic Power Rule* and *Solving Logarithmic Equations* knowledge points $$ \begin{aligned} 3 \ln 4 &= 2 \ln x \ \ln(4^3) &= \ln(x^2) \ 64 &= x^2 \ x &= 8 \quad (\text{since } x > 0 \text{ for } \ln x) \end{aligned} $$ ## Solve the second logarithmic equation Using the *Inverse Properties of Logarithms* and *Solving Logarithmic Equations* knowledge points $$ \begin{aligned} 6 \ln e &= e^{\ln 2x} \ 6(1) &= 2x \ 6 &= 2x \ x &= 3 \end{aligned} $$ ## Question 1 (A) $\{6\}$

(B) $\{-8, 8\}$

(C) $\{8\}$ ## Question 2 (A) $\{2\}$

(B) $\{3\}$

(C) $\{6\}$

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

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QUESTION IMAGE

Question

Explanation:

Solve the first logarithmic equation

Solve the second logarithmic equation

Answer:

Question 1

Question 2