convert each equation into its equivalent logarithmic form.

a) $2^3 = 8$
- $\log_2(8) = 3$
- $\log_2(3) = 8$
- $\log_3(8) = 2$
- none of the above

b) $4^3 = 64$
- $\log_4(64) = 3$
- $\log_4(3) = 64$
- $\log_3(64) = 4$
- none of the above

Question

convert each equation into its equivalent logarithmic form.

a) $2^3 = 8$
- $\log_2(8) = 3$
- $\log_2(3) = 8$
- $\log_3(8) = 2$
- none of the above

b) $4^3 = 64$
- $\log_4(64) = 3$
- $\log_4(3) = 64$
- $\log_3(64) = 4$
- 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 Equations", "Exponential Equations" ], "new_concepts": [ "Logarithmic Form Conversion" ], "current_concepts": [ "Exponential Equations", "Logarithmic Equations", "Logarithmic Form Conversion" ] } ## Convert the first exponential equation to logarithmic form $$ \begin{aligned} &b^y = x \iff \log_b(x) = y \ &2^3 = 8 \iff \log_2(8) = 3 \end{aligned} $$ ## Convert the second exponential equation to logarithmic form $$ \begin{aligned} &b^y = x \iff \log_b(x) = y \ &4^3 = 64 \iff \log_4(64) = 3 \end{aligned} $$ ## Question 1 O $\log_2(8) = 3$

O $\log_2(3) = 8$

O $\log_3(8) = 2$

O None of the above ## Question 2 O $\log_4(64) = 3$

O $\log_4(3) = 64$

O $\log_3(64) = 4$

O 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 first exponential equation to logarithmic form

Convert the second exponential equation to logarithmic form

Answer:

Question 1

Question 2