what is the solution to the equation $2^{x+4} - 12 = 20$?

$x = 0$
$x = 1$
$x = 2$
$x = 9$

Question

what is the solution to the equation $2^{x+4} - 12 = 20$?

$x = 0$
$x = 1$
$x = 2$
$x = 9$

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 Algebraically", "Solving Exponential Equations" ], "new_concepts": [], "current_concepts": [ "Solving Exponential Equations Algebraically", "Solving Exponential Equations" ] } ## Isolate the exponential term Using the *Solving Exponential Equations* knowledge point $$ \begin{aligned} 2^{x+4} - 12 &= 20 \ 2^{x+4} &= 20 + 12 \ 2^{x+4} &= 32 \end{aligned} $$ ## Express both sides with a common base Using the *Solving Exponential Equations Algebraically* knowledge point $$ \begin{aligned} 32 &= 2^5 \ 2^{x+4} &= 2^5 \end{aligned} $$ ## Equate exponents and solve for x Using the *Solving Exponential Equations Algebraically* knowledge point $$ \begin{aligned} x + 4 &= 5 \ x &= 5 - 4 \ x &= 1 \end{aligned} $$

$x = 0$

$x = 1$

$x = 2$

$x = 9$

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

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QUESTION IMAGE

Question

Explanation:

Isolate the exponential term

Express both sides with a common base

Equate exponents and solve for x

Answer: