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.
$x = -4$ and $x = 4$

what is the solution to $2 \ln x = 4 \ln 2$?
$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.
$x = -4$ and $x = 4$

what is the solution to $2 \ln x = 4 \ln 2$?
$x = $

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "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", "Extraneous Solutions" ] } ## Apply the logarithmic power rule Using the *Logarithmic Power Rule* knowledge point $$ \begin{aligned} 2 \ln x &= \ln(x^2) \ 4 \ln 2 &= \ln(2^4) = \ln 16 \end{aligned} $$ ## Set up the equation for potential solutions Using the *Solving Logarithmic Equations* knowledge point $$ \begin{aligned} \ln(x^2) &= \ln 16 \ x^2 &= 16 \ x &= \pm 4 \end{aligned} $$ ## Check for extraneous solutions Using the *Solving Logarithmic Equations* knowledge point $$ \begin{aligned} &\text{For } x = -4: \ln(-4) \text{ is undefined since the domain of } \ln(x) \text{ is } x > 0. \ &\text{For } x = 4: \ln(4) \text{ is defined.} \end{aligned} $$ Thus, the only valid solution is $x = 4$. What is the solution to $2 \ln x = 4 \ln 2$? $x =$ 4 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Solving Logarithmic Equations" ] }

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QUESTION IMAGE

Question

Explanation:

Apply the logarithmic power rule

Set up the equation for potential solutions

Check for extraneous solutions

Answer: