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

Question

Accepted Answer

{ "quality": "clear", "question_count": 1, "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" ] } ## Convert to exponential form Using the *Solving Logarithmic Equations* knowledge point $$ \begin{aligned} &\log_{4}(7t + 2) = 2 \ &7t + 2 = 4^2 \end{aligned} $$ ## Simplify the power Using the *Solving Logarithmic Equations* knowledge point $$ 7t + 2 = 16 $$ ## Isolate the variable term Using the *Solving Logarithmic Equations* knowledge point $$ \begin{aligned} &7t = 16 - 2 \ &7t = 14 \end{aligned} $$ ## Solve for t Using the *Solving Logarithmic Equations* knowledge point $$ \begin{aligned} &t = \frac{14}{7} \ &t = 2 \end{aligned} $$ ## Verify the solution Using the *Solving Logarithmic Equations* knowledge point $$ \begin{aligned} &\text{Check: } \log_{4}(7(2) + 2) = \log_{4}(14 + 2) = \log_{4}(16) = 2 \quad (\text{Valid}) \end{aligned} $$ Solve: $\log_{4}(7t + 2) = 2$ $t =$ 2 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Solving Logarithmic Equations" ] }

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Question

Explanation:

Convert to exponential form

Simplify the power

Isolate the variable term

Solve for t

Verify the solution

Answer: