the expression $\frac{\log \frac{1}{3}}{\log 2}$ is the result of applying the change of base formula to a logarithmic expression. which could be the original expression?

$\log_{\frac{1}{3}} 2$
$\log_{\frac{1}{2}} 3$
$\log_2 \frac{1}{3}$
$\log_3 \frac{1}{2}$

Question

the expression $\frac{\log \frac{1}{3}}{\log 2}$ is the result of applying the change of base formula to a logarithmic expression. which could be the original expression?

$\log_{\frac{1}{3}} 2$
$\log_{\frac{1}{2}} 3$
$\log_2 \frac{1}{3}$
$\log_3 \frac{1}{2}$

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": [ "Change of Base Formula" ], "new_concepts": [], "current_concepts": [ "Change of Base Formula", "Logarithmic Evaluation" ] } ## Identify the given expression and formula Using the *Change of Base Formula* knowledge point $$ \frac{\log \frac{1}{3}}{\log 2} $$ The change of base formula states: $$ \log_b a = \frac{\log_c a}{\log_c b} $$ ## Map the components to find the original expression Using the *Change of Base Formula* knowledge point $$ \begin{aligned} a &= \frac{1}{3} \ b &= 2 \ \frac{\log \frac{1}{3}}{\log 2} &= \log_2 \frac{1}{3} \end{aligned} $$

(A) $\log_{\frac{1}{3}} 2$

(B) $\log_{\frac{1}{2}} 3$

(C) $\log_2 \frac{1}{3}$

(D) $\log_3 \frac{1}{2}$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Change of Base Formula" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the given expression and formula

Map the components to find the original expression

Answer: