question 19

the sum $\log_2(9) + \log_2(5)$ can also be expressed as $\underline{\quad\quad\quad\quad}$.

* $\log_2(14)$
* $\log_4(45)$
* $\log_4(14)$
* $\log_2(45)$

Question

question 19

the sum $\log_2(9) + \log_2(5)$ can also be expressed as $\underline{\quad\quad\quad\quad}$.

* $\log_2(14)$
* $\log_4(45)$
* $\log_4(14)$
* $\log_2(45)$

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": [ "Product Rule for Logarithms" ], "new_concepts": [], "current_concepts": [ "Logarithm Properties", "Product Rule for Logarithms" ] } ## Apply the product rule for logarithms Using the *Product Rule for Logarithms* knowledge point $$ \log_b(M) + \log_b(N) = \log_b(M \cdot N) $$ ## Simplify the expression Using the *Product Rule for Logarithms* knowledge point $$ \begin{aligned} \log_2(9) + \log_2(5) &= \log_2(9 \cdot 5) \ &= \log_2(45) \end{aligned} $$

(A) $\log_2(14)$

(B) $\log_4(45)$

(C) $\log_4(14)$

(D) $\log_2(45)$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Product Rule for Logarithms" ] }

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QUESTION IMAGE

Question

Explanation:

Apply the product rule for logarithms

Simplify the expression

Answer: