if $3^{-3x+6} = 27^{x+4}$, then $x$ equals ______.

a.) 5
b.) -2
c.) -1
d.) 0.5

Question

if $3^{-3x+6} = 27^{x+4}$, then $x$ equals ______.

a.) 5
b.) -2
c.) -1
d.) 0.5

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Linear Equations" ], "new_concepts": [ "Exponential Equations" ], "current_concepts": [ "Linear Equations", "Exponential Equations" ] } ## Express both sides with the same base $$ \begin{aligned} 27 &= 3^3 \ 3^{-3x+6} &= (3^3)^{x+4} \ 3^{-3x+6} &= 3^{3(x+4)} \end{aligned} $$ ## Equate the exponents $$ \begin{aligned} -3x + 6 &= 3(x + 4) \ -3x + 6 &= 3x + 12 \end{aligned} $$ ## Solve for x $$ \begin{aligned} -6x &= 6 \ x &= -1 \end{aligned} $$

a.) 5

b.) -2

c.) -1

d.) 0.5

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

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Express both sides with the same base

Equate the exponents

Solve for x

Answer: