solve the equation $3^x = 27$. if no solution exists, enter none.

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{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Exponential Equations" ], "new_concepts": [], "current_concepts": [ "Exponential Equations" ] } ## Express both sides with a common base $$ \begin{aligned} 3^x &= 27 \ 3^x &= 3^3 \end{aligned} $$ ## Equate the exponents $$ x = 3 $$ Solve the equation $3^x = 27$. If no solution exists, enter None. $x = 3$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Exponential Equations" ] }

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Explanation:

Express both sides with a common base

Equate the exponents

Answer: