which equation has $x = -6$ as the solution?

$\log_{x} 36 = 2$
$\log_{3} (2x - 9) = 3$
$\log_{3} 216 = x$
$\log_{3} (-2x - 3) = 2$

Question

which equation has $x = -6$ as the solution?

$\log_{x} 36 = 2$
$\log_{3} (2x - 9) = 3$
$\log_{3} 216 = x$
$\log_{3} (-2x - 3) = 2$

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": [ "Solving Logarithmic Equations" ], "new_concepts": [], "current_concepts": [ "Solving Logarithmic Equations", "Logarithmic Evaluation" ] } ## Test the first equation Using the *Solving Logarithmic Equations* knowledge point $$ \begin{aligned} &\log_{x} 36 = 2 \implies x^2 = 36 \implies x = 6 \quad (x > 0, x e 1) \end{aligned} $$ ## Test the second equation Using the *Solving Logarithmic Equations* knowledge point $$ \begin{aligned} &\log_{3} (2x - 9) = 3 \implies 2x - 9 = 3^3 \implies 2x - 9 = 27 \implies 2x = 36 \implies x = 18 \end{aligned} $$ ## Test the third equation Using the *Solving Logarithmic Equations* knowledge point $$ \begin{aligned} &\log_{3} 216 = x \implies 3^x = 216 \implies x \approx 4.89 \end{aligned} $$ ## Test the fourth equation Using the *Solving Logarithmic Equations* knowledge point $$ \begin{aligned} &\log_{3} (-2x - 3) = 2 \implies -2x - 3 = 3^2 \implies -2x - 3 = 9 \implies -2x = 12 \implies x = -6 \end{aligned} $$

(A) $\log_{x} 36 = 2$

(B) $\log_{3} (2x - 9) = 3$

(C) $\log_{3} 216 = x$

(D) $\log_{3} (-2x - 3) = 2$

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

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