what are the potential solutions of $\ln(x^2 - 25) = 0$?

$x = \pm\sqrt{13}$
$x = \pm 5$
$x = \pm\sqrt{26}$
$x = \pm 10$

Question

what are the potential solutions of $\ln(x^2 - 25) = 0$?

$x = \pm\sqrt{13}$
$x = \pm 5$
$x = \pm\sqrt{26}$
$x = \pm 10$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Logarithmic Equations" ], "new_concepts": [], "current_concepts": [ "Logarithmic Equations", "Solving Quadratic Equations" ] } ## Convert logarithmic equation to exponential form $$ \begin{aligned} \ln(x^2 - 25) &= 0 \ x^2 - 25 &= e^0 \ x^2 - 25 &= 1 \end{aligned} $$ ## Solve for x $$ \begin{aligned} x^2 &= 26 \ x &= \pm\sqrt{26} \end{aligned} $$ ## Verify solutions in the domain $$ \begin{aligned} (\pm\sqrt{26})^2 - 25 = 26 - 25 = 1 > 0 \end{aligned} $$

(A) $x = \pm\sqrt{13}$

(B) $x = \pm5$

(C) $x = \pm\sqrt{26}$

(D) $x = \pm10$

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

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QUESTION IMAGE

Question

Explanation:

Convert logarithmic equation to exponential form

Solve for x

Verify solutions in the domain

Answer: