which logarithmic equation is equivalent to $8^2 = 64$?

$2 = \log_{8} 64$
$2 = \log_{64} 8$
$8 = \log_{2} 64$
$64 = \log_{2} 8$

Question

which logarithmic equation is equivalent to $8^2 = 64$?

$2 = \log_{8} 64$
$2 = \log_{64} 8$
$8 = \log_{2} 64$
$64 = \log_{2} 8$

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 Functions", "Logarithmic Evaluation" ], "new_concepts": [], "current_concepts": [ "Logarithmic Functions", "Logarithmic Evaluation", "Logarithmic and Exponential Inverses" ] } ## Identify the exponential base, exponent, and result Using the *Logarithmic Functions* knowledge point $$ \begin{aligned} &\text{Given equation: } 8^2 = 64\ &\text{Base } (b) = 8\ &\text{Exponent } (x) = 2\ &\text{Result } (y) = 64 \end{aligned} $$ ## Convert to logarithmic form Using the *Logarithmic and Exponential Inverses* knowledge points $$ \begin{aligned} &b^x = y \iff \log_b(y) = x\ &8^2 = 64 \iff \log_8(64) = 2 \end{aligned} $$ ## Match with the given options Using the *Logarithmic Evaluation* knowledge point $$ 2 = \log_8(64) $$

(A) $2 = \log_{8}64$

(B) $2 = \log_{64}8$

(C) $8 = \log_{2}64$

(D) $64 = \log_{2}8$

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

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QUESTION IMAGE

Question

Explanation:

Identify the exponential base, exponent, and result

Convert to logarithmic form

Match with the given options

Answer: