Solve (3^{2x} – 3^{x+2} = 3^{x+1} – 27)
-
A.
1 or 0 -
B.
1 or 2 -
C.
1 or -2 -
D.
-1 or 2
Correct Answer: Option B
Explanation
(3^{2x} – 3^{x+2} = 3^{x+1} – 27)
= ((3^{x})^{2} – (3^{x}).(3^{2}) = (3^{x}).(3^{1}) – 27)
Let (3^{x}) be B; we have
= (B^{2} – 9B – 3B + 27 = B^{2} – 12B + 27 = 0).
Solving the equation, we have B = 3 or 9.
(3^{x} = 3) or (3^{x} = 9)
(3^{x} = 3^{1}) or (3^{x} = 3^{2})
Equating, we have x = 1 or 2.