evaluate: $\log_{125} 5$
- $\frac{1}{3}$
- $\frac{1}{2}$
- $\frac{2}{3}$

evaluate: $\log_{16} 64$
- $\frac{1}{3}$
- $\frac{2}{3}$
- $\frac{3}{2}$

Question

evaluate: $\log_{125} 5$
- $\frac{1}{3}$
- $\frac{1}{2}$
- $\frac{2}{3}$

evaluate: $\log_{16} 64$
- $\frac{1}{3}$
- $\frac{2}{3}$
- $\frac{3}{2}$

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 logarithmic expression Using the *Logarithmic Evaluation* knowledge point $$ \begin{aligned} &\text{Let } x = \log_{125}5\ &125^x = 5\ &(5^3)^x = 5^1\ &5^{3x} = 5^1\ &3x = 1 \implies x = \frac{1}{3} \end{aligned} $$ ## Evaluate the second logarithmic expression Using the *Logarithmic Evaluation* knowledge point $$ \begin{aligned} &\text{Let } y = \log_{16}64\ &16^y = 64\ &(4^2)^y = 4^3\ &4^{2y} = 4^3\ &2y = 3 \implies y = \frac{3}{2} \end{aligned} $$ ## Question 1 (A) $\frac{1}{3}$

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

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

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

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

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

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Evaluate the first logarithmic expression

Evaluate the second logarithmic expression

Answer:

Question 1

Question 2