if $5^{3b-1} = 5^{b-3}$, what is the value of $b$?

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Question

if $5^{3b-1} = 5^{b-3}$, what is the value of $b$?

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Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Exponential Equations", "One-to-One Property" ], "current_concepts": [ "Exponential Equations", "One-to-One Property" ] } ## Equate the exponents using the one-to-one property of exponential functions $$ 3b - 1 = b - 3 $$ ## Solve the linear equation for b $$ \begin{aligned} 2b - 1 &= -3 \ 2b &= -2 \ b &= -1 \end{aligned} $$

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{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Exponential Equations" ] }

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QUESTION IMAGE

Question

Explanation:

Equate the exponents using the one-to-one property of exponential functions

Solve the linear equation for b

Answer: