to solve the equation $2^{x - 1} - 7 = 9$, first add 7 to each side.

what common base can be used to rewrite each side of the resulting equation?

2
4
16
32

Question

to solve the equation $2^{x - 1} - 7 = 9$, first add 7 to each side.

what common base can be used to rewrite each side of the resulting equation?

2
4
16
32

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" ], "new_concepts": [], "current_concepts": [ "Solving Exponential Equations Algebraically" ] } ## Isolate the exponential term Using the *Solving Exponential Equations Algebraically* knowledge point $$ \begin{aligned} 2^{x-1} - 7 &= 9 \ 2^{x-1} &= 16 \end{aligned} $$ ## Identify the common base Using the *Solving Exponential Equations Algebraically* knowledge point $$ \begin{aligned} 16 &= 2^4 \ 2^{x-1} &= 2^4 \end{aligned} $$ The common base is $2$.

2

4

16

32

{ "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

Identify the common base

Answer: