solve: $4 \ln x = 2 \ln 25$
- $x = 5$
- $x = 25$
- $x = 625$

solve: $3 \ln x = \ln 216$
- $x = 3$
- $x = 6$
- $x = 72$

Question

solve: $4 \ln x = 2 \ln 25$
- $x = 5$
- $x = 25$
- $x = 625$

solve: $3 \ln x = \ln 216$
- $x = 3$
- $x = 6$
- $x = 72$

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" ] } ## Solve the first logarithmic equation Using the *Logarithmic Power Rule* and *Solving Logarithmic Equations* knowledge points $$ \begin{aligned} 4 \ln x &= 2 \ln 25 \ \ln(x^4) &= \ln(25^2) \ x^4 &= 625 \ x &= 5 \quad (x > 0) \end{aligned} $$ ## Solve the second logarithmic equation Using the *Logarithmic Power Rule* and *Solving Logarithmic Equations* knowledge points $$ \begin{aligned} 3 \ln x &= \ln 216 \ \ln(x^3) &= \ln 216 \ x^3 &= 216 \ x &= 6 \quad (x > 0) \end{aligned} $$ ## Question 1 x = 5

x = 25

x = 625 ## Question 2 x = 3

x = 6

x = 72

{ "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