solve: $12^{x^2 + 5x - 4} = 12^{2x + 6}$

$x = 2$
$x = -5$
$x = 2, x = -5$
no solution

Question

solve: $12^{x^2 + 5x - 4} = 12^{2x + 6}$

$x = 2$
$x = -5$
$x = 2, x = -5$
no solution

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Exponential Equations", "One-to-One Property" ], "new_concepts": [], "current_concepts": [ "Exponential Equations", "One-to-One Property", "Quadratic Equations" ] } ## Equate the exponents using the one-to-one property $$ x^2 + 5x - 4 = 2x + 6 $$ ## Rearrange into standard quadratic form $$ \begin{aligned} x^2 + 5x - 2x - 4 - 6 &= 0 \ x^2 + 3x - 10 &= 0 \end{aligned} $$ ## Solve the quadratic equation by factoring $$ \begin{aligned} (x + 5)(x - 2) &= 0 \ x = -5 \quad &\text{or} \quad x = 2 \end{aligned} $$

$x = 2$

$x = -5$

$x = 2, x = -5$

no solution

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

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QUESTION IMAGE

Question

Explanation:

Equate the exponents using the one-to-one property

Rearrange into standard quadratic form

Solve the quadratic equation by factoring

Answer: