solve: $\log_{4}(7t + 2) = 2$
$t = $

solve: $\log_{x}343 = 3$
$x = $

Question

solve: $\log_{4}(7t + 2) = 2$
$t = $

solve: $\log_{x}343 = 3$
$x = $

Accepted Answer

{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Solving Logarithmic Equations" ], "new_concepts": [], "current_concepts": [ "Solving Logarithmic Equations", "Logarithmic Evaluation" ] } ## Convert to exponential form Using the *Solving Logarithmic Equations* knowledge point $$ \begin{aligned} &\log_4(7t + 2) = 2 \implies 7t + 2 = 4^2\ &\log_x 343 = 3 \implies x^3 = 343 \end{aligned} $$ ## Solve the first equation for t Using the *Solving Logarithmic Equations* knowledge point $$ \begin{aligned} &7t + 2 = 16\ &7t = 14\ &t = 2 \end{aligned} $$ ## Solve the second equation for x Using the *Solving Logarithmic Equations* knowledge point $$ \begin{aligned} &x^3 = 343\ &x = \sqrt[3]{343}\ &x = 7 \end{aligned} $$ ## Question 1 Solve: $\log_4(7t + 2) = 2$ $t =$ 2 ## Question 2 Solve: $\log_x 343 = 3$ $x =$ 7 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Solving Logarithmic Equations" ] }

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QUESTION IMAGE

Question

Explanation:

Convert to exponential form

Solve the first equation for t

Solve the second equation for x

Answer:

Question 1

Question 2