9. solve $5^{x-1} = \frac{1}{125}$ for x.

$x = 2$

$x = -\frac{1}{2}$

$x = -2$

$x = \frac{1}{2}$

Question

9. solve $5^{x-1} = \frac{1}{125}$ for x.

$x = 2$

$x = -\frac{1}{2}$

$x = -2$

$x = \frac{1}{2}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Exponent Rules", "Exponential Equations" ], "new_concepts": [], "current_concepts": [ "Exponent Rules", "Exponential Equations" ] } ## Express both sides with a common base Using the *Exponent Rules* and *Exponential Equations* knowledge points $$ \begin{aligned} &125 = 5^3 \ &\frac{1}{125} = \frac{1}{5^3} = 5^{-3} \end{aligned} $$ ## Set exponents equal and solve Using the *Exponential Equations* and *Linear Equation Solving* knowledge points $$ \begin{aligned} &5^{x-1} = 5^{-3} \ &x - 1 = -3 \ &x = -2 \end{aligned} $$

(A) $x = 2$

(B) $x = -\frac{1}{2}$

(C) $x = -2$

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

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

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QUESTION IMAGE

Question

Explanation:

Express both sides with a common base

Set exponents equal and solve

Answer: