if $5 + 20 * 2^{2-3x} = 10 * 2^{-2x} + 5$, what is the value of $x$?

-3
-2
2
3

Question

if $5 + 20 * 2^{2-3x} = 10 * 2^{-2x} + 5$, what is the value of $x$?

-3
-2
2
3

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Exponential Equations" ], "new_concepts": [], "current_concepts": [ "Exponential Equations" ] } ## Simplify the equation by subtracting constants and dividing $$ \begin{aligned} 5 + 20 \cdot 2^{2-3x} &= 10 \cdot 2^{-2x} + 5 \ 20 \cdot 2^{2-3x} &= 10 \cdot 2^{-2x} \ 2 \cdot 2^{2-3x} &= 2^{-2x} \end{aligned} $$ ## Express both sides with base 2 $$ \begin{aligned} 2^1 \cdot 2^{2-3x} &= 2^{-2x} \ 2^{1 + 2 - 3x} &= 2^{-2x} \ 2^{3-3x} &= 2^{-2x} \end{aligned} $$ ## Equate exponents and solve for x $$ \begin{aligned} 3 - 3x &= -2x \ 3 &= 3x - 2x \ x &= 3 \end{aligned} $$

(A) $-3$

(B) $-2$

(C) $2$

(D) $3$

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

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QUESTION IMAGE

Question

Explanation:

Simplify the equation by subtracting constants and dividing

Express both sides with base 2

Equate exponents and solve for x

Answer: