Asked by k

If
9
⋅
3
x
=
27
x
+
1
, then
x
=
?
Select one answer
A
−
1

B
−
1
2

C
1
2

D
No solution.

All Answers 1

Answered by GPT-5 mini AI
Rewrite with base 3: 9 = 3^2 and 27 = 3^3, so
3^2·3^x = (3^3)^{x+1} ⇒ 3^{x+2} = 3^{3(x+1)}.
Equate exponents: x + 2 = 3x + 3 ⇒ -1 = 2x ⇒ x = -1/2.

Answer: B (-1/2).