c) $5^3 = 125$

$\bigcirc$ $\log_3(125) = 5$
$\bigcirc$ $\log_5(3) = 125$
$\bigcirc$ $\log_5(125) = 3$
$\bigcirc$ none of the above

d) $3^4 = 81$

$\bigcirc$ $\log_4(81) = 3$
$\bigcirc$ $\log_3(81) = 4$
$\bigcirc$ $\log_3(4) = 81$
$\bigcirc$ none of the above

Question

c) $5^3 = 125$

$\bigcirc$ $\log_3(125) = 5$
$\bigcirc$ $\log_5(3) = 125$
$\bigcirc$ $\log_5(125) = 3$
$\bigcirc$ none of the above

d) $3^4 = 81$

$\bigcirc$ $\log_4(81) = 3$
$\bigcirc$ $\log_3(81) = 4$
$\bigcirc$ $\log_3(4) = 81$
$\bigcirc$ none of the above

Accepted Answer

{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Logarithmic Form Conversion" ], "new_concepts": [], "current_concepts": [ "Logarithmic Form Conversion" ] } ## Convert the exponential equation in part c $$ \begin{aligned} &b^y = x \iff \log_b(x) = y \ &5^3 = 125 \iff \log_5(125) = 3 \end{aligned} $$ ## Convert the exponential equation in part d $$ \begin{aligned} &b^y = x \iff \log_b(x) = y \ &3^4 = 81 \iff \log_3(81) = 4 \end{aligned} $$ ## Question 1 (A) $\log_3(125) = 5$

(B) $\log_5(3) = 125$

(C) $\log_5(125) = 3$

(D) None of the above ## Question 2 (A) $\log_4(81) = 3$

(B) $\log_3(81) = 4$

(C) $\log_3(4) = 81$

(D) None of the above

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

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QUESTION IMAGE

Question

Explanation:

Convert the exponential equation in part c

Convert the exponential equation in part d

Answer:

Question 1

Question 2