evaluate: $\log_{12}12$
0
1
12
-1
complete

evaluate: $\log_{27}9$
$\frac{1}{3}$
$\frac{2}{3}$
$\frac{3}{2}$
$-\frac{1}{3}$
done

Question

evaluate: $\log_{12}12$
0
1
12
-1
complete

evaluate: $\log_{27}9$
$\frac{1}{3}$
$\frac{2}{3}$
$\frac{3}{2}$
$-\frac{1}{3}$
done

Accepted Answer

{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Logarithmic Evaluation" ], "new_concepts": [], "current_concepts": [ "Logarithmic Evaluation" ] } ## Evaluate the first logarithm Using the *Logarithmic Evaluation* knowledge point $$ \log_{12}12 = 1 $$ ## Evaluate the second logarithm Using the *Logarithmic Evaluation* knowledge point $$ \begin{aligned} x &= \log_{27}9 \ 27^x &= 9 \ (3^3)^x &= 3^2 \ 3^{3x} &= 3^2 \ 3x &= 2 \ x &= \frac{2}{3} \end{aligned} $$ ## Question 1 (A) 0

(B) 1

(C) 12

(D) -1 ## Question 2 (A) $\frac{1}{3}$

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

(C) $\frac{3}{2}$

(D) $-\frac{1}{3}$

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

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QUESTION IMAGE

Question

Explanation:

Evaluate the first logarithm

Evaluate the second logarithm

Answer:

Question 1

Question 2