what is the value of $x$ if $5^{x+2} = 5^9$?

$x = -11$
$x = -7$
$x = 7$
$x = 11$

Question

what is the value of $x$ if $5^{x+2} = 5^9$?

$x = -11$
$x = -7$
$x = 7$
$x = 11$

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": [ "Solving Exponential Equations" ], "new_concepts": [], "current_concepts": [ "Solving Exponential Equations", "Linear Equations" ] } ## Equate the exponents Using the *Solving Exponential Equations* knowledge point $$ \begin{aligned} 5^{x+2} &= 5^9 \ x + 2 &= 9 \end{aligned} $$ ## Solve for x Using the *Linear Equations* knowledge point $$ \begin{aligned} x &= 9 - 2 \ x &= 7 \end{aligned} $$

$x = -11$

$x = -7$

$x = 7$

$x = 11$

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

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Question

Explanation:

Equate the exponents

Solve for x

Answer: