what is the value of $\log_{7} 343$?

* $-3$
* $-\frac{1}{3}$
* $\frac{1}{3}$
* $3$

Question

what is the value of $\log_{7} 343$?

* $-3$
* $-\frac{1}{3}$
* $\frac{1}{3}$
* $3$

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 Evaluation" ], "new_concepts": [], "current_concepts": [ "Logarithmic Evaluation" ] } ## Set up the logarithmic equation Using the **Logarithmic Evaluation** knowledge point $$ x = \log_{7}{343} \iff 7^x = 343 $$ ## Express 343 as a power of 7 Using the **Logarithmic Evaluation** knowledge point $$ \begin{aligned} 7^1 &= 7 \ 7^2 &= 49 \ 7^3 &= 343 \end{aligned} $$ ## Solve for x Using the **Logarithmic Evaluation** knowledge point $$ 7^x = 7^3 \implies x = 3 $$

(A) $-3$

(B) $-\frac{1}{3}$

(C) $\frac{1}{3}$

(D) $3$

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

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QUESTION IMAGE

Question

Explanation:

Set up the logarithmic equation

Express 343 as a power of 7

Solve for x

Answer: