solve: $2 \ln 3 = \ln(x - 4)$
$x = 9$
$x = 10$
$x = 13$

list the potential solutions to $2 \ln x = 4 \ln 2$ from least to greatest.
$x = $ and $x = $

Question

solve: $2 \ln 3 = \ln(x - 4)$
$x = 9$
$x = 10$
$x = 13$

list the potential solutions to $2 \ln x = 4 \ln 2$ from least to greatest.
$x = $   and $x = $

Accepted Answer

{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Solving Logarithmic Equations", "Logarithmic Power Rule" ], "new_concepts": [], "current_concepts": [ "Solving Logarithmic Equations", "Logarithmic Power Rule" ] } ## Solve the first logarithmic equation Using the *Logarithmic Power Rule* and *Solving Logarithmic Equations* knowledge points $$ \begin{aligned} 2 \ln 3 &= \ln(x - 4) \ \ln(3^2) &= \ln(x - 4) \ \ln 9 &= \ln(x - 4) \ 9 &= x - 4 \ x &= 13 \end{aligned} $$ ## Solve the second logarithmic equation Using the *Logarithmic Power Rule* and *Solving Logarithmic Equations* knowledge points $$ \begin{aligned} 2 \ln x &= 4 \ln 2 \ \ln(x^2) &= \ln(2^4) \ x^2 &= 16 \ x &= \pm 4 \end{aligned} $$ ## Check for extraneous solutions Using the *Solving Logarithmic Equations* knowledge point $$ \begin{aligned} &\text{For } 2 \ln x = 4 \ln 2, \text{ the domain requires } x > 0.\ &\text{Thus, } x = -4 \text{ is extraneous.}\ &\text{The only valid potential solution is } x = 4. \end{aligned} $$ ## Question 1 (A) $x = 9$

(B) $x = 10$

(C) $x = 13$ ## Question 2 List the potential solutions to $2 \ln x = 4 \ln 2$ from least to greatest. $x =$ -4 and $x =$ 4 { "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Algebra", "Solving Logarithmic Equations" ] }

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QUESTION IMAGE

Question

Explanation:

Solve the first logarithmic equation

Solve the second logarithmic equation

Check for extraneous solutions

Answer:

Question 1

Question 2