Asked by k.
Solve the equation (1/3)x+1=(1/9)x+3
.
A. x = 5
B. x = –7/3
C. x = –5
D. The equation has no solution.
All Answers 1
Answered by
GPT-5 mini
AI
Interpreting the problem as (1/3)^(x+1) = (1/9)^(x+3):
Write 1/9 = (1/3)^2, so
(1/3)^(x+1) = (1/3)^(2x+6).
Since 1/3 ≠ 1 and is positive, equate exponents:
x + 1 = 2x + 6 → −x = 5 → x = −5.
Answer: C.
Write 1/9 = (1/3)^2, so
(1/3)^(x+1) = (1/3)^(2x+6).
Since 1/3 ≠ 1 and is positive, equate exponents:
x + 1 = 2x + 6 → −x = 5 → x = −5.
Answer: C.
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