solve: $4 \ln x = 2 \ln 25$

$x = 5$
$x = 25$
$x = 625$

Question

solve: $4 \ln x = 2 \ln 25$

$x = 5$
$x = 25$
$x = 625$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Solving Logarithmic Equations" ], "new_concepts": [], "current_concepts": [ "Solving Logarithmic Equations", "Logarithmic Power Rule" ] } ## Isolate the logarithmic term $$ \begin{aligned} 4 \ln x &= 2 \ln 25 \ \ln x &= \frac{2}{4} \ln 25 \ \ln x &= \frac{1}{2} \ln 25 \end{aligned} $$ ## Apply the logarithmic power rule $$ \begin{aligned} \ln x &= \ln(25^{1/2}) \ \ln x &= \ln 5 \end{aligned} $$ ## Solve for x $$ x = 5 $$

(A) $x = 5$

(B) $x = 25$

(C) $x = 625$

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

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Isolate the logarithmic term

Apply the logarithmic power rule

Solve for x

Answer: