what is the solution to $\ln(x^2 - 16) = 0$?

$x = \pm\sqrt{17}$
$x = \pm 4$
$x = \pm\sqrt{32}$

Question

what is the solution to $\ln(x^2 - 16) = 0$?

$x = \pm\sqrt{17}$
$x = \pm 4$
$x = \pm\sqrt{32}$

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 Functions" ] } ## Rewrite the logarithmic equation in exponential form Using the **Solving Logarithmic Equations** knowledge point $$ \begin{aligned} &\ln(x^2 - 16) = 0 \ &x^2 - 16 = e^0 \ &x^2 - 16 = 1 \end{aligned} $$ ## Solve the quadratic equation for x Using the **Solving Logarithmic Equations** knowledge point $$ \begin{aligned} &x^2 = 17 \ &x = \pm\sqrt{17} \end{aligned} $$ ## Verify the solutions in the original domain Using the **Solving Logarithmic Equations** knowledge point $$ \begin{aligned} &x^2 - 16 > 0 \implies 17 - 16 = 1 > 0 \end{aligned} $$

(A) $x = \pm\sqrt{17}$

(B) $x = \pm 4$

(C) $x = \pm\sqrt{32}$

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

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QUESTION IMAGE

Question

Explanation:

Rewrite the logarithmic equation in exponential form

Solve the quadratic equation for x

Verify the solutions in the original domain

Answer: