2. solve $3^{4x} 9^{x-3}$ for $x$.

$x -\frac{1}{3}$

$x = \frac{1}{3}$

$x -1$

$x 3$

Question

2. solve $3^{4x} > 9^{x-3}$ for $x$.

$x > -\frac{1}{3}$

$x = \frac{1}{3}$

$x > -1$

$x > 3$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Exponent Rules", "Solving Linear Inequalities" ], "new_concepts": [ "Exponential Inequalities" ], "current_concepts": [ "Exponent Rules", "Solving Linear Inequalities", "Exponential Inequalities" ] } ## Express both sides with a common base $$ \begin{aligned} &3^{4x} > (3^2)^{x-3} \ &3^{4x} > 3^{2(x-3)} \end{aligned} $$ ## Set up the inequality for the exponents $$ \begin{aligned} &4x > 2(x-3) \ &4x > 2x - 6 \end{aligned} $$ ## Solve for x $$ \begin{aligned} &2x > -6 \ &x > -3 \end{aligned} $$

(A) $x > -\frac{1}{3}$

(B) $x = \frac{1}{3}$

(C) $x > -3$

(D) $x > 3$

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

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QUESTION IMAGE

Question

Explanation:

Express both sides with a common base

Set up the inequality for the exponents

Solve for x

Answer: