what equation is equivalent to $9^{x - 3} = 729$?

$9^{x - 3} = 9^{81}$
$9^{x - 3} = 9^3$
$3^{x - 3} = 3^6$
$3^{2x - 3} = 3^6$

solve: $9^{x - 3} = 729$
$x =$

Question

what equation is equivalent to $9^{x - 3} = 729$?

$9^{x - 3} = 9^{81}$
$9^{x - 3} = 9^3$
$3^{x - 3} = 3^6$
$3^{2x - 3} = 3^6$

solve: $9^{x - 3} = 729$
$x =$

Accepted Answer

{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Solving Exponential Equations Algebraically" ], "new_concepts": [], "current_concepts": [ "Solving Exponential Equations Algebraically" ] } ## Express 729 as a power of 9 Using the *Solving Exponential Equations Algebraically* knowledge point $$ 9^3 = 9 \times 9 \times 9 = 81 \times 9 = 729 $$ ## Identify the equivalent equation Using the *Solving Exponential Equations Algebraically* knowledge point $$ \begin{aligned} &9^{x-3} = 729 \ &9^{x-3} = 9^3 \end{aligned} $$ ## Solve for x Using the *Solving Exponential Equations Algebraically* knowledge point $$ \begin{aligned} x - 3 &= 3 \ x &= 6 \end{aligned} $$ ## Question 1 (A) $9^{x-3} = 9^{81}$

(B) $9^{x-3} = 9^3$

(C) $3^{x-3} = 3^6$

(D) $3^{2x-3} = 3^6$ ## Question 2 $x =$ 6 { "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Algebra", "Solving Exponential Equations Algebraically" ] }

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QUESTION IMAGE

Question

Explanation:

Express 729 as a power of 9

Identify the equivalent equation

Solve for x

Answer:

Question 1

Question 2