what is the value of (x) if (9^{x-1} - 2 = 25)?

(x = \frac{1}{2})

(x = 2)

(x = \frac{5}{2})

(x = 4)

Question

what is the value of (x) if (9^{x-1} - 2 = 25)?

(x = \frac{1}{2})

(x = 2)

(x = \frac{5}{2})

(x = 4)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Exponential Equations" ], "new_concepts": [], "current_concepts": [ "Exponential Equations" ] } ## Isolate the exponential term $$ \begin{aligned} 9^{x-1} - 2 &= 25 \ 9^{x-1} &= 27 \end{aligned} $$ ## Express with a common base $$ \begin{aligned} (3^2)^{x-1} &= 3^3 \ 3^{2(x-1)} &= 3^3 \end{aligned} $$ ## Solve for x $$ \begin{aligned} 2(x-1) &= 3 \ 2x - 2 &= 3 \ 2x &= 5 \ x &= \frac{5}{2} \end{aligned} $$

(A) $x = \frac{1}{2}$

(B) $x = 2$

(C) $x = \frac{5}{2}$

(D) $x = 4$

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

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QUESTION IMAGE

Question

Explanation:

Isolate the exponential term

Express with a common base

Solve for x

Answer: