which equation is equivalent to $4^{x+3} = 64$?

$2^{x+6} = 2^4$
$2^{2x+6} = 2^6$
$4^{2x+6} = 4^2$
$4^{x+3} = 4^6$

Question

which equation is equivalent to $4^{x+3} = 64$?

$2^{x+6} = 2^4$
$2^{2x+6} = 2^6$
$4^{2x+6} = 4^2$
$4^{x+3} = 4^6$

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", "Exponent Rules" ] } ## Rewrite the base of the exponential term Using the *Solving Exponential Equations* knowledge point $$ \begin{aligned} 4^{x+3} &= (2^2)^{x+3} \ &= 2^{2(x+3)} \ &= 2^{2x+6} \end{aligned} $$ ## Rewrite the constant term with base 2 Using the *Solving Exponential Equations* knowledge point $$ 64 = 2^6 $$ ## Equate the rewritten expressions Using the *Solving Exponential Equations* knowledge point $$ 2^{2x+6} = 2^6 $$

(A) $2^{x+6} = 2^4$

(B) $2^{2x+6} = 2^6$

(C) $4^{2x+6} = 4^2$

(D) $4^{x+3} = 4^6$

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

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Rewrite the base of the exponential term

Rewrite the constant term with base 2

Equate the rewritten expressions

Answer: