devonte used the change of base formula to approximate $\log_{8} 25$. which expression did devonte use?

$\log \frac{8}{25}$

$\frac{\log 8}{\log 25}$

$\log \frac{25}{8}$

$\frac{\log 25}{\log 8}$

Question

devonte used the change of base formula to approximate $\log_{8} 25$. which expression did devonte use?

$\log \frac{8}{25}$

$\frac{\log 8}{\log 25}$

$\log \frac{25}{8}$

$\frac{\log 25}{\log 8}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Change of Base Formula" ], "new_concepts": [], "current_concepts": [ "Change of Base Formula", "Logarithmic Functions" ] } ## State the change of base formula $$ \log_{b} a = \frac{\log_{c} a}{\log_{c} b} $$ ## Substitute the given values $$ \begin{aligned} &b = 8, \quad a = 25, \quad c = 10\ &\log_{8} 25 = \frac{\log 25}{\log 8} \end{aligned} $$

(A) $\log \frac{8}{25}$

(B) $\frac{\log 8}{\log 25}$

(C) $\log \frac{25}{8}$

(D) $\frac{\log 25}{\log 8}$

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

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QUESTION IMAGE

Question

Explanation:

State the change of base formula

Substitute the given values

Answer: