evaluate: $\log_{125} 5$

$\bigcirc$ $\frac{1}{3}$

$\bigcirc$ $\frac{1}{2}$

$\bigcirc$ $\frac{2}{3}$

Question

evaluate: $\log_{125} 5$

$\bigcirc$ $\frac{1}{3}$

$\bigcirc$ $\frac{1}{2}$

$\bigcirc$ $\frac{2}{3}$

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": [ "Logarithmic Evaluation" ], "new_concepts": [], "current_concepts": [ "Logarithmic Evaluation" ] } ## Express the base and argument with a common base Using the *Logarithmic Evaluation* knowledge point $$ \begin{aligned} &125 = 5^3\ &5 = 5^1 \end{aligned} $$ ## Apply the change of base or power property Using the *Logarithmic Evaluation* knowledge point $$ \log_{125} 5 = \log_{5^3} 5^1 = \frac{1}{3} \log_5 5 = \frac{1}{3} $$

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

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

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

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

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QUESTION IMAGE

Question

Explanation:

Express the base and argument with a common base

Apply the change of base or power property

Answer: