Solve the given equation ((log_{3} x)^{2} – 6(log_{3} x) + 9 = 0)

A.
27 
B.
9 
C.
(frac{1}{27}) 
D.
18 
E.
81
Correct Answer: Option A
Explanation
((log_{3} x)^{2} – 6(log_{3} x) + 9 = 0)
Let (log_{3} x = a).
(a^{2} – 6a + 9 = 0)
(a^{2} – 3a – 3a + 9 = 0)
(a(a – 3) – 3(a – 3) = 0)
((a – 3)(a – 3) = 0)
(implies a = 3 (twice))
(log_{3} x = 3 implies x = 3^{3} = 27)