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

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)